# List of all pairs of integers (x,y) such that
# x + y is a square, gcd(x,y) is square-free, x >= y, and the only primes dividing x and y lie in S,
# for all sets S = {2, 3, 5, p},
# where p ranges over all other primes less or equal to 31.
# It contains 1760 pairs (x,y), some of which may appear for more than one S.
# Format: "(x,y)".
# Computing this list took 4504 seconds.
# Authors: Rafael von Känel and Benjamin Matschke, 2015.
# License: Creative commons 3.0 by-nc.
#
#
# S = {2, 3, 5, 7}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(3,-3)
(3,-2)
(3,1)
(4,-3)
(5,-5)
(5,-4)
(5,-1)
(5,4)
(6,-6)
(6,-5)
(6,-2)
(6,3)
(7,-7)
(7,-6)
(7,-3)
(7,2)
(8,-7)
(8,1)
(9,-8)
(9,-5)
(9,7)
(10,-10)
(10,-9)
(10,-6)
(10,-1)
(10,6)
(12,-3)
(14,-14)
(14,-10)
(14,-5)
(14,2)
(15,-15)
(15,-14)
(15,-6)
(15,1)
(15,10)
(16,-15)
(16,-7)
(16,9)
(18,-14)
(18,-2)
(18,7)
(20,5)
(21,-21)
(21,-20)
(21,-12)
(21,-5)
(21,4)
(21,15)
(24,-15)
(24,1)
(25,-24)
(25,-21)
(25,-16)
(25,-9)
(25,24)
(27,-2)
(28,-27)
(28,-3)
(28,21)
(30,-30)
(30,-21)
(30,-14)
(30,-5)
(30,6)
(32,-7)
(35,-35)
(35,-10)
(35,1)
(35,14)
(36,-35)
(40,-15)
(40,9)
(42,-42)
(42,-6)
(42,7)
(45,-20)
(45,4)
(48,1)
(49,-48)
(49,-45)
(49,-40)
(49,-24)
(49,15)
(49,32)
(50,-49)
(50,-14)
(50,-1)
(50,14)
(54,-50)
(54,-5)
(54,10)
(56,-7)
(56,25)
(60,-35)
(60,21)
(63,-14)
(63,1)
(64,-63)
(64,-15)
(70,-70)
(70,-54)
(70,-45)
(70,-21)
(70,-6)
(70,30)
(72,49)
(75,6)
(80,1)
(81,-80)
(81,-56)
(81,-32)
(81,40)
(84,-75)
(84,-35)
(84,-3)
(90,10)
(96,-15)
(96,25)
(98,2)
(100,21)
(105,-105)
(105,-96)
(105,-80)
(105,-56)
(105,-24)
(105,-5)
(105,16)
(105,64)
(112,-63)
(112,9)
(120,1)
(120,49)
(120,105)
(125,-4)
(126,-125)
(126,-5)
(126,70)
(128,-7)
(135,-35)
(135,-14)
(144,25)
(147,-3)
(150,-6)
(160,-135)
(160,9)
(162,-98)
(162,7)
(168,1)
(175,-126)
(175,-54)
(175,-6)
(175,21)
(175,81)
(189,-140)
(189,-125)
(189,-20)
(189,7)
(189,100)
(196,-75)
(196,-27)
(210,-210)
(210,-14)
(210,15)
(224,-175)
(224,1)
(225,-224)
(225,-56)
(225,64)
(240,-15)
(240,49)
(245,-20)
(250,-81)
(250,-54)
(250,6)
(256,-175)
(256,-135)
(256,105)
(270,-245)
(270,-14)
(280,9)
(280,81)
(288,1)
(294,-150)
(294,-125)
(294,-5)
(294,30)
(324,-35)
(336,25)
(336,105)
(343,-243)
(343,-54)
(343,18)
(360,1)
(375,-294)
(375,-14)
(384,-375)
(405,-5)
(420,21)
(441,-320)
(441,-80)
(441,400)
(448,-7)
(448,81)
(480,49)
(486,-125)
(486,-2)
(490,-486)
(490,-90)
(490,-6)
(490,135)
(504,25)
(512,-343)
(525,-84)
(525,4)
(576,49)
(625,-576)
(625,-504)
(625,-336)
(625,-96)
(625,-49)
(625,216)
(625,336)
(630,-5)
(640,-15)
(675,1)
(686,-10)
(729,-560)
(729,-245)
(729,-200)
(729,112)
(729,640)
(735,-6)
(750,-686)
(750,-21)
(840,1)
(896,625)
(945,-896)
(945,-320)
(945,16)
(945,280)
(960,-735)
(960,1)
(1024,-735)
(1024,-63)
(1029,-500)
(1029,-300)
(1029,-5)
(1029,60)
(1120,105)
(1120,729)
(1134,-350)
(1215,-686)
(1215,10)
(1225,-864)
(1225,-384)
(1225,144)
(1250,686)
(1260,-35)
(1344,25)
(1372,-3)
(1458,-14)
(1500,21)
(1536,-15)
(1600,81)
(1680,1)
(1701,-20)
(1701,700)
(1750,-1701)
(1750,14)
(1792,-567)
(1800,49)
(1920,105)
(2025,784)
(2160,49)
(2205,4)
(2400,1)
(2401,-2400)
(2401,-1440)
(2401,-720)
(2401,-192)
(2401,200)
(2401,1080)
(2430,70)
(2625,-1536)
(2625,-224)
(2625,-24)
(2625,1344)
(2800,9)
(3024,1)
(3150,-14)
(3200,49)
(3375,2401)
(3430,-405)
(3456,25)
(3840,2401)
(3969,-125)
(3969,256)
(4050,-686)
(4096,-375)
(4096,945)
(4374,250)
(4375,-4374)
(4480,9)
(4704,625)
(5040,1)
(5145,-5120)
(5145,-384)
(5145,480)
(6250,-9)
(6561,-6272)
(6561,-5600)
(6561,-320)
(6804,-875)
(7840,81)
(8505,-1280)
(8505,-224)
(9375,1029)
(9408,1)
(9800,1)
(10206,-5)
(10240,-1215)
(10368,2401)
(10584,25)
(11250,-14)
(12544,225)
(13230,-5)
(14175,-14)
(14336,-175)
(14406,-6)
(15309,-12500)
(15625,-10584)
(15625,-1701)
(15625,504)
(15625,1536)
(16128,1)
(16384,-14175)
(16807,13122)
(17500,189)
(18144,625)
(18225,-3584)
(18750,294)
(21504,105)
(23625,1024)
(24010,15)
(25920,1)
(26250,-6)
(30618,7)
(32768,-7)
(33614,-125)
(35721,-32000)
(43740,-1715)
(43750,-486)
(46305,-80)
(48384,15625)
(49000,729)
(50625,-896)
(55566,-3125)
(59049,1960)
(59049,7000)
(59535,1)
(60025,-1944)
(63000,1)
(64000,9)
(65625,-57344)
(69120,49)
(76545,71680)
(82944,30625)
(83349,2500)
(85750,-486)
(109375,-1134)
(117649,-97200)
(117649,48000)
(128625,256)
(129654,-78125)
(137200,59049)
(137781,-140)
(140625,-43904)
(168070,30)
(179200,6561)
(196830,-33614)
(201600,1)
(201684,-1875)
(214375,-6)
(243000,49)
(245760,-735)
(252105,-24576)
(262144,5145)
(390625,-112896)
(688905,-5)
(1058841,-20480)
(1440000,2401)
(1640625,336)
(4214784,25)
(4782969,4375)
(5764801,-9600)
(19140625,-17496)
(23049600,1)
(76545000,1)
(199290375,-686)
#
# S = {2, 3, 5, 11}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(3,-3)
(3,-2)
(3,1)
(4,-3)
(5,-5)
(5,-4)
(5,-1)
(5,4)
(6,-6)
(6,-5)
(6,-2)
(6,3)
(8,1)
(9,-8)
(9,-5)
(10,-10)
(10,-9)
(10,-6)
(10,-1)
(10,6)
(11,-11)
(11,-10)
(11,-2)
(11,5)
(12,-11)
(12,-3)
(15,-15)
(15,-11)
(15,-6)
(15,1)
(15,10)
(16,-15)
(16,9)
(18,-2)
(20,-11)
(20,5)
(22,-22)
(22,-18)
(22,-6)
(22,3)
(24,-15)
(24,1)
(25,-24)
(25,-16)
(25,-9)
(25,11)
(25,24)
(27,-11)
(27,-2)
(27,22)
(30,-30)
(30,-5)
(30,6)
(33,-33)
(33,-32)
(33,-24)
(33,-8)
(33,3)
(33,16)
(36,-11)
(40,-15)
(40,9)
(44,5)
(45,-44)
(45,-20)
(45,4)
(48,1)
(48,33)
(50,-1)
(54,-50)
(54,-5)
(54,10)
(55,-55)
(55,-54)
(55,-30)
(55,-6)
(55,9)
(55,45)
(60,-11)
(64,-55)
(64,-15)
(66,-66)
(66,-50)
(66,-30)
(66,-2)
(66,15)
(66,55)
(75,-66)
(75,-11)
(75,6)
(80,-55)
(80,1)
(81,-80)
(81,-32)
(81,40)
(88,33)
(88,81)
(90,10)
(96,-15)
(96,25)
(99,-50)
(99,1)
(99,22)
(100,-99)
(110,-110)
(110,-10)
(110,11)
(120,1)
(121,-120)
(121,-96)
(121,-72)
(121,-40)
(121,48)
(121,75)
(125,-121)
(125,-44)
(125,-4)
(125,44)
(132,-11)
(135,-110)
(135,121)
(144,25)
(150,-6)
(160,-135)
(160,9)
(165,-165)
(165,-44)
(165,4)
(165,60)
(176,-55)
(180,-11)
(192,33)
(198,-2)
(220,-99)
(220,5)
(225,-176)
(225,64)
(240,-15)
(240,121)
(243,-242)
(250,-81)
(250,-54)
(250,6)
(256,-135)
(256,33)
(264,25)
(288,1)
(297,-176)
(297,-128)
(297,-8)
(297,64)
(300,-11)
(320,121)
(324,-275)
(330,-330)
(330,-6)
(352,9)
(360,1)
(363,-2)
(375,66)
(384,-375)
(396,-275)
(405,-44)
(405,-5)
(405,220)
(440,1)
(484,45)
(486,-125)
(486,-2)
(495,-11)
(528,1)
(540,-11)
(550,-486)
(550,-66)
(594,-110)
(605,20)
(625,-576)
(625,-264)
(625,-96)
(625,216)
(640,-15)
(675,1)
(704,25)
(720,121)
(726,-150)
(726,-50)
(726,3)
(729,-704)
(729,-440)
(729,-200)
(729,55)
(729,640)
(825,-704)
(825,-384)
(825,-96)
(825,16)
(825,264)
(880,81)
(891,-50)
(960,1)
(972,-11)
(1024,-495)
(1024,825)
(1056,33)
(1056,625)
(1089,-800)
(1089,-128)
(1100,-11)
(1210,-810)
(1210,-54)
(1210,15)
(1215,10)
(1280,-55)
(1331,-1250)
(1375,-891)
(1375,-6)
(1500,-1331)
(1536,-15)
(1584,625)
(1600,81)
(1620,-1331)
(1728,121)
(1875,726)
(2025,-176)
(2187,22)
(2200,9)
(2376,25)
(2400,1)
(2500,-99)
(2662,-162)
(2673,-2048)
(2673,352)
(2700,-1331)
(2970,55)
(3025,-216)
(3025,2304)
(3125,11)
(3375,-11)
(3456,25)
(3520,-495)
(3600,121)
(3630,-30)
(3645,-2420)
(3840,-1815)
(3993,-512)
(3993,-24)
(3993,768)
(4096,-375)
(4224,1)
(4374,250)
(4500,-11)
(5324,5)
(5346,-1250)
(5625,-2816)
(5632,297)
(5940,-11)
(6250,-9)
(6561,-320)
(6655,-2430)
(7920,1)
(8019,-275)
(9375,-726)
(9801,400)
(10125,484)
(10240,-1215)
(10935,-1331)
(11880,1)
(12288,33)
(13750,891)
(14080,81)
(14641,-12960)
(14641,-9600)
(14641,-480)
(14641,243)
(14641,2000)
(15125,4)
(15625,-14256)
(15625,-1936)
(15625,1536)
(16384,-16335)
(19200,121)
(19360,6561)
(19602,-2)
(20625,-176)
(22000,6561)
(24057,-32)
(25920,1)
(28125,-5324)
(32805,-44)
(34375,594)
(39600,1)
(45056,-1375)
(45375,-6)
(46464,625)
(58080,1)
(58806,-31250)
(59049,-968)
(59049,35200)
(64000,9)
(66825,-2816)
(66825,256)
(67584,20625)
(71874,-50)
(75625,-31104)
(99825,-98304)
(123904,18225)
(138240,14641)
(146410,-486)
(151875,-1331)
(161051,-250)
(187500,-11)
(235224,1)
(267300,-11)
(390625,107811)
(483153,-128)
(515625,-1536)
(531441,-70400)
(601425,-180224)
(756250,-354294)
(1670625,1048576)
(1771561,-405000)
(2052864,625)
(6655000,6561)
(7144929,-5120000)
(21897216,390625)
#
# S = {2, 3, 5, 13}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(3,-3)
(3,-2)
(3,1)
(4,-3)
(5,-5)
(5,-4)
(5,-1)
(5,4)
(6,-6)
(6,-5)
(6,-2)
(6,3)
(8,1)
(9,-8)
(9,-5)
(10,-10)
(10,-9)
(10,-6)
(10,-1)
(10,6)
(12,-3)
(13,-13)
(13,-12)
(13,-9)
(13,-4)
(13,3)
(13,12)
(15,-15)
(15,-6)
(15,1)
(15,10)
(16,-15)
(16,9)
(18,-2)
(20,5)
(24,-15)
(24,1)
(25,-24)
(25,-16)
(25,-9)
(25,24)
(26,-26)
(26,-25)
(26,-10)
(26,-1)
(26,10)
(27,-26)
(27,-2)
(30,-30)
(30,-26)
(30,-5)
(30,6)
(36,13)
(39,-39)
(39,-30)
(39,-3)
(39,10)
(39,25)
(40,-39)
(40,-15)
(40,9)
(45,-20)
(45,4)
(48,-39)
(48,1)
(50,-1)
(52,-27)
(52,-3)
(54,-50)
(54,-5)
(54,10)
(64,-39)
(64,-15)
(65,-65)
(65,-64)
(65,-40)
(65,-16)
(65,-1)
(65,16)
(75,-39)
(75,-26)
(75,6)
(78,-78)
(78,3)
(80,1)
(81,-80)
(81,-65)
(81,-32)
(81,40)
(90,-65)
(90,-26)
(90,10)
(96,-15)
(96,25)
(104,65)
(108,13)
(117,4)
(117,52)
(120,-39)
(120,1)
(125,-4)
(130,-130)
(130,-81)
(130,-30)
(130,-9)
(130,39)
(144,25)
(150,-6)
(156,-75)
(156,13)
(160,-135)
(160,-39)
(160,9)
(160,65)
(169,-160)
(169,-144)
(169,-120)
(169,-48)
(169,-25)
(169,27)
(169,120)
(192,169)
(195,-195)
(195,-26)
(195,1)
(195,30)
(208,-39)
(208,81)
(225,-104)
(225,64)
(234,-65)
(240,-15)
(243,13)
(250,-234)
(250,-169)
(250,-81)
(250,-54)
(250,6)
(250,39)
(250,234)
(256,-135)
(270,130)
(288,1)
(325,-324)
(325,-156)
(325,-36)
(325,-1)
(325,36)
(351,10)
(351,325)
(360,1)
(360,169)
(384,-375)
(390,-390)
(390,10)
(400,-351)
(400,-39)
(405,-5)
(416,25)
(480,-39)
(486,-125)
(486,-2)
(520,-351)
(520,9)
(585,-416)
(585,40)
(585,256)
(624,1)
(625,-624)
(625,-576)
(625,-96)
(625,104)
(625,216)
(640,-351)
(640,-15)
(640,585)
(650,26)
(675,1)
(676,-675)
(702,-26)
(729,-200)
(729,-104)
(729,640)
(768,-39)
(810,-26)
(832,9)
(845,-4)
(936,25)
(960,1)
(1000,-39)
(1014,10)
(1014,75)
(1014,750)
(1024,-975)
(1024,65)
(1200,169)
(1215,10)
(1521,160)
(1536,-15)
(1560,-39)
(1600,81)
(1625,-256)
(1625,-104)
(1690,-729)
(1690,-90)
(1690,-9)
(1690,810)
(1875,-26)
(2025,-1664)
(2028,-3)
(2080,729)
(2106,10)
(2187,-338)
(2197,-972)
(2197,-81)
(2197,12)
(2400,1)
(2496,-975)
(2560,-2535)
(2560,-351)
(2600,1)
(2808,1)
(3250,-1)
(3328,-3159)
(3456,25)
(4000,-3159)
(4096,-375)
(4160,65)
(4212,13)
(4225,-256)
(4320,169)
(4374,250)
(4800,-39)
(5184,4225)
(5200,729)
(5265,-1040)
(5265,64)
(5616,625)
(5760,169)
(6075,-4394)
(6240,1)
(6250,-9)
(6250,3159)
(6400,1521)
(6561,-4160)
(6561,-320)
(6591,-30)
(6656,1625)
(6750,-26)
(7290,-65)
(7680,-6591)
(8125,-729)
(8125,156)
(8320,-39)
(9126,6250)
(9984,625)
(10240,-1215)
(10240,-39)
(10985,-4096)
(10985,40)
(13689,4000)
(14625,16)
(15625,-13689)
(15625,-3744)
(15625,1536)
(16000,-6591)
(16384,-3159)
(16640,1)
(18954,-16250)
(20800,-351)
(21870,-845)
(21970,-21870)
(24375,-39)
(25000,-351)
(25920,1)
(26244,325)
(28431,130)
(28561,-14400)
(28561,-5760)
(30000,-6591)
(39546,6250)
(40625,-1024)
(40960,5265)
(48000,-39)
(52000,-3159)
(57122,-1)
(59049,13312)
(64000,9)
(65536,-2535)
(81000,28561)
(81250,-59049)
(97344,625)
(105625,-1296)
(108160,81)
(114244,-675)
(136890,10)
(142155,-26)
(156250,-1014)
(169000,6561)
(171366,30)
(203125,-113724)
(248832,169)
(256000,-255879)
(257049,10240)
(390625,-2496)
(390625,303264)
(421200,1)
(426465,2560)
(455625,2704)
(531441,-260000)
(851968,-39)
(1038336,25)
(1113879,156250)
(1171875,1014)
(1184625,-425984)
(1228800,-1113879)
(1406250,-4394)
(1560000,1)
(1825200,1)
(4782969,87880)
(4804839,25)
(4826809,-87480)
(10485760,-59319)
#
# S = {2, 3, 5, 17}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(3,-3)
(3,-2)
(3,1)
(4,-3)
(5,-5)
(5,-4)
(5,-1)
(5,4)
(6,-6)
(6,-5)
(6,-2)
(6,3)
(8,1)
(9,-8)
(9,-5)
(10,-10)
(10,-9)
(10,-6)
(10,-1)
(10,6)
(12,-3)
(15,-15)
(15,-6)
(15,1)
(15,10)
(16,-15)
(16,9)
(17,-17)
(17,-16)
(17,-8)
(17,-1)
(17,8)
(18,-17)
(18,-2)
(20,5)
(24,-15)
(24,1)
(25,-24)
(25,-16)
(25,-9)
(25,24)
(27,-2)
(30,-30)
(30,-5)
(30,6)
(32,17)
(34,-34)
(34,-30)
(34,-25)
(34,-18)
(34,-9)
(34,2)
(34,15)
(34,30)
(40,-15)
(40,9)
(45,-20)
(45,4)
(48,1)
(50,-34)
(50,-1)
(51,-51)
(51,-50)
(51,-15)
(51,-2)
(51,30)
(54,-50)
(54,-5)
(54,10)
(60,-51)
(64,-15)
(64,17)
(75,6)
(80,1)
(81,-80)
(81,-32)
(81,-17)
(81,40)
(85,-85)
(85,-81)
(85,-60)
(85,-36)
(85,-4)
(85,15)
(85,36)
(90,10)
(96,-15)
(96,25)
(100,-51)
(102,-102)
(102,-2)
(120,1)
(125,-4)
(135,34)
(136,-135)
(136,-15)
(144,25)
(150,-6)
(153,-128)
(153,-32)
(153,16)
(153,136)
(160,-135)
(160,9)
(162,34)
(170,-170)
(170,-1)
(204,85)
(225,64)
(225,136)
(240,-15)
(250,-81)
(250,-54)
(250,6)
(255,-255)
(255,-30)
(255,1)
(255,34)
(256,-255)
(256,-135)
(270,-170)
(272,17)
(288,1)
(289,-288)
(289,-240)
(289,-225)
(289,-120)
(289,-64)
(289,72)
(289,240)
(306,-50)
(306,-17)
(340,-51)
(360,1)
(375,-51)
(384,-375)
(405,-5)
(425,-256)
(425,-136)
(425,-64)
(425,16)
(450,34)
(459,-170)
(459,25)
(480,-255)
(486,-125)
(486,-2)
(510,-510)
(512,17)
(540,85)
(544,-375)
(544,-255)
(544,-15)
(544,81)
(578,-2)
(625,-576)
(625,-544)
(625,-96)
(625,51)
(625,216)
(640,-15)
(675,1)
(729,-680)
(729,-200)
(729,640)
(750,34)
(800,289)
(816,-375)
(816,25)
(850,-729)
(850,-9)
(850,306)
(960,1)
(1080,289)
(1088,1)
(1215,10)
(1224,1)
(1224,625)
(1250,-289)
(1360,-135)
(1360,9)
(1377,-1088)
(1377,-8)
(1377,1024)
(1445,-1)
(1536,-15)
(1600,81)
(1734,-1250)
(1734,30)
(1920,289)
(2040,-15)
(2125,-1836)
(2125,-9)
(2176,-1215)
(2176,225)
(2176,425)
(2400,1)
(2550,51)
(2601,-200)
(2754,-50)
(2890,-81)
(2890,135)
(2916,2125)
(3264,-15)
(3400,81)
(3456,25)
(4096,-375)
(4096,3825)
(4374,250)
(4590,34)
(4624,-135)
(4913,128)
(5440,-1215)
(6250,-9)
(6561,-4352)
(6561,-320)
(6561,1360)
(6885,4)
(6885,340)
(6936,-375)
(7225,-1296)
(8704,-3375)
(9375,34)
(9826,-4050)
(9826,-2430)
(9826,-25)
(9826,375)
(10200,1)
(10240,-1215)
(10625,-16)
(11560,-10935)
(12393,-512)
(13122,-578)
(15360,-4335)
(15625,-7344)
(15625,1536)
(16384,-255)
(18225,544)
(18750,14739)
(20736,289)
(21250,-2754)
(21870,34)
(23409,-12800)
(24565,-540)
(24786,-10625)
(25920,1)
(34425,544)
(34816,-20655)
(34816,153)
(37179,-31250)
(39304,-9375)
(44217,-32768)
(46240,-15)
(52224,-9375)
(54000,289)
(64000,9)
(65025,1024)
(65280,-255)
(70227,-2)
(73440,1)
(73984,50625)
(78336,625)
(83521,-57600)
(83521,-1152)
(87040,-15)
(95625,8704)
(98415,9826)
(122825,-1024)
(127500,-51)
(139264,-135)
(261120,1)
(265625,-262144)
(332928,1)
(390625,-176256)
(557056,-10935)
(628864,-15)
(835210,-59049)
(1003833,2176)
(1328125,-26244)
(1336336,-273375)
(1360000,6561)
(1775616,-9375)
(4782969,1156000)
(20225376,15625)
(22781250,9826)
#
# S = {2, 3, 5, 19}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(3,-3)
(3,-2)
(3,1)
(4,-3)
(5,-5)
(5,-4)
(5,-1)
(5,4)
(6,-6)
(6,-5)
(6,-2)
(6,3)
(8,1)
(9,-8)
(9,-5)
(10,-10)
(10,-9)
(10,-6)
(10,-1)
(10,6)
(12,-3)
(15,-15)
(15,-6)
(15,1)
(15,10)
(16,-15)
(16,9)
(18,-2)
(19,-19)
(19,-18)
(19,-15)
(19,-10)
(19,-3)
(19,6)
(20,-19)
(20,5)
(24,-15)
(24,1)
(25,-24)
(25,-16)
(25,-9)
(25,24)
(27,-2)
(30,-30)
(30,-5)
(30,6)
(30,19)
(38,-38)
(38,-2)
(40,-15)
(40,9)
(45,-20)
(45,4)
(45,19)
(48,1)
(50,-1)
(54,-50)
(54,-38)
(54,-5)
(54,10)
(57,-57)
(57,-48)
(57,-32)
(57,-8)
(57,24)
(64,-15)
(64,57)
(75,6)
(76,-75)
(76,-27)
(76,5)
(76,45)
(80,1)
(81,-80)
(81,-32)
(81,19)
(81,40)
(90,10)
(95,-95)
(95,5)
(96,-95)
(96,-15)
(96,25)
(100,-19)
(114,-114)
(114,-50)
(114,30)
(120,-95)
(120,1)
(125,-76)
(125,-4)
(125,19)
(144,-95)
(144,25)
(150,-114)
(150,-6)
(150,19)
(160,-135)
(160,9)
(171,-50)
(171,-2)
(171,25)
(190,-190)
(190,-90)
(190,6)
(190,171)
(216,-95)
(225,64)
(228,-3)
(240,-15)
(250,-81)
(250,-54)
(250,6)
(256,-135)
(270,19)
(285,-285)
(285,-60)
(285,4)
(285,76)
(288,1)
(304,-135)
(304,-15)
(304,57)
(304,225)
(320,-95)
(342,19)
(360,1)
(361,-360)
(361,-240)
(361,-192)
(361,-72)
(361,80)
(380,-19)
(384,-375)
(384,-95)
(384,57)
(405,-380)
(405,-5)
(456,-375)
(456,-95)
(456,-15)
(475,-114)
(475,9)
(475,54)
(480,361)
(486,-125)
(486,-2)
(486,190)
(486,475)
(513,-512)
(513,-152)
(513,16)
(570,-570)
(570,6)
(600,361)
(625,-576)
(625,-456)
(625,-96)
(625,216)
(640,-15)
(675,1)
(720,-95)
(729,-608)
(729,-200)
(729,640)
(760,-135)
(760,81)
(864,361)
(960,1)
(1024,-855)
(1026,-2)
(1083,6)
(1215,10)
(1216,-1215)
(1216,-855)
(1216,-375)
(1216,9)
(1350,19)
(1368,1)
(1425,19)
(1425,96)
(1425,256)
(1444,-75)
(1444,405)
(1520,1)
(1536,-15)
(1539,-1250)
(1539,-95)
(1600,81)
(1824,25)
(1824,1425)
(1900,-1539)
(1944,-95)
(2166,-50)
(2166,750)
(2304,-95)
(2400,1)
(2430,-1805)
(2500,-1539)
(2736,-2375)
(3040,-15)
(3125,-1444)
(3249,-3200)
(3456,25)
(3610,-10)
(3610,486)
(3645,76)
(4096,-375)
(4320,-95)
(4374,250)
(4617,-128)
(4750,1026)
(4864,-375)
(4864,2025)
(5184,-2375)
(5625,304)
(5776,-3375)
(6144,-5415)
(6144,1425)
(6250,-9)
(6561,-1520)
(6561,-320)
(6859,-6075)
(6859,-4050)
(6859,-135)
(6859,30)
(6859,3750)
(7220,5)
(7296,625)
(7600,6561)
(8664,-15)
(9025,384)
(9120,-95)
(10125,76)
(10240,-1215)
(11520,361)
(11875,6)
(12160,-10935)
(12825,4864)
(13824,-2375)
(14440,-1215)
(15625,1536)
(15625,10944)
(16416,15625)
(18240,-15)
(18750,19)
(19456,-135)
(20577,-128)
(22800,1)
(23085,19)
(24576,-2375)
(24624,25)
(25920,1)
(27436,1125)
(29184,57)
(30720,-95)
(32400,361)
(34656,-9375)
(35625,96)
(36480,1)
(39366,-18050)
(39366,-950)
(39366,6859)
(41553,19456)
(43776,-95)
(58320,-34295)
(59049,-45125)
(64000,9)
(65536,513)
(68590,54)
(69984,-59375)
(72000,361)
(76000,729)
(93750,-114)
(98304,-34295)
(124659,-50)
(130321,-1440)
(243000,130321)
(263169,-2048)
(279936,-95)
(296875,-13851)
(311296,-7695)
(311296,35625)
(312500,-19)
(369664,-1215)
(519840,1)
(701784,15625)
(781926,-781250)
(1048576,-438615)
(1050624,1)
(1245184,-759375)
(1476225,4864)
(1923750,19)
(2991816,-2375)
(3188646,11875)
(3258025,1990656)
(4980736,-3375)
(5909760,1)
(7023616,-5859375)
(14786560,59049)
(22265625,116736)
(633881344,-15)
#
# S = {2, 3, 5, 23}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(3,-3)
(3,-2)
(3,1)
(4,-3)
(5,-5)
(5,-4)
(5,-1)
(5,4)
(6,-6)
(6,-5)
(6,-2)
(6,3)
(8,1)
(9,-8)
(9,-5)
(10,-10)
(10,-9)
(10,-6)
(10,-1)
(10,6)
(12,-3)
(15,-15)
(15,-6)
(15,1)
(15,10)
(16,-15)
(16,9)
(18,-2)
(20,5)
(23,-23)
(23,2)
(24,-23)
(24,-15)
(24,1)
(25,-24)
(25,-16)
(25,-9)
(25,24)
(27,-23)
(27,-2)
(30,-30)
(30,-5)
(30,6)
(32,-23)
(40,-15)
(40,9)
(45,-20)
(45,4)
(46,-46)
(46,-45)
(46,-30)
(46,-10)
(46,3)
(46,18)
(48,-23)
(48,1)
(50,-46)
(50,-1)
(54,-50)
(54,-5)
(54,10)
(54,46)
(64,-15)
(69,-69)
(69,-60)
(69,-20)
(69,-5)
(69,12)
(72,-23)
(75,6)
(75,46)
(75,69)
(80,1)
(81,-80)
(81,-32)
(81,40)
(90,10)
(96,-15)
(96,25)
(100,69)
(115,-115)
(115,-90)
(115,-15)
(115,6)
(115,54)
(115,81)
(120,1)
(125,-4)
(138,-138)
(138,6)
(144,-23)
(144,25)
(150,-69)
(150,-6)
(150,46)
(160,-135)
(160,9)
(184,-135)
(184,-15)
(192,-23)
(225,64)
(230,-230)
(230,-5)
(240,-15)
(243,46)
(250,-81)
(250,-54)
(250,6)
(256,-207)
(256,-135)
(288,1)
(345,-345)
(345,-320)
(345,-120)
(345,16)
(345,96)
(345,184)
(360,1)
(384,-375)
(384,-23)
(384,345)
(405,-5)
(414,-125)
(414,115)
(460,69)
(486,-230)
(486,-125)
(486,-2)
(529,-480)
(529,-360)
(529,-240)
(529,-45)
(529,96)
(529,200)
(529,432)
(552,-23)
(575,-46)
(575,1)
(576,-575)
(621,-500)
(621,-92)
(621,4)
(625,-621)
(625,-576)
(625,-184)
(625,-96)
(625,216)
(640,-15)
(648,-23)
(675,1)
(690,-690)
(729,-368)
(729,-200)
(729,640)
(736,-375)
(736,-207)
(736,225)
(864,-575)
(864,-23)
(960,1)
(1024,345)
(1104,-575)
(1104,-375)
(1104,-15)
(1150,-621)
(1150,6)
(1152,529)
(1215,10)
(1250,46)
(1458,-1058)
(1536,-575)
(1536,-15)
(1600,81)
(1656,25)
(1840,-1215)
(1840,9)
(1944,-575)
(2025,184)
(2048,-23)
(2070,46)
(2208,1)
(2400,1)
(2944,-135)
(2944,81)
(3105,-80)
(3174,-3125)
(3174,75)
(3456,25)
(3726,-5)
(3750,-3174)
(4050,46)
(4096,-375)
(4374,115)
(4374,250)
(4416,345)
(4416,625)
(4600,729)
(4761,-1280)
(4800,529)
(5290,486)
(5400,529)
(5589,2875)
(6250,-9)
(6561,-320)
(6912,-23)
(7360,-135)
(7500,69)
(8280,1)
(8625,24)
(10240,-1215)
(11040,-15)
(11776,-10935)
(11776,-9375)
(12288,-12167)
(12696,-375)
(13248,-23)
(14904,-14375)
(15625,1536)
(15870,6)
(17496,-12167)
(17664,25)
(21160,-135)
(24334,-2430)
(24334,2)
(24334,16875)
(24576,-14375)
(24576,-7935)
(25875,46)
(25920,1)
(26496,-575)
(27945,-14720)
(27945,4096)
(28566,-5)
(28750,4374)
(33856,-30375)
(34992,-23)
(36501,-20)
(43125,-276)
(47104,-46575)
(47104,-15)
(50301,-125)
(59049,-58880)
(60835,-810)
(64000,9)
(71875,486)
(77625,11776)
(82944,-575)
(89424,-23)
(98304,8625)
(104976,-14375)
(124416,13225)
(182505,1536)
(184000,59049)
(215625,17664)
(279841,240000)
(330625,2304)
(354294,-2645)
(357696,15625)
(385641,10000)
(388125,4)
(389344,-1215)
(390625,-203136)
(390625,-9936)
(390625,59616)
(531441,-423200)
(583200,279841)
(1048576,-46575)
(1324800,1)
(1620000,529)
(3188646,1150)
(4100625,188416)
(11193640,-7971615)
(12058624,3105)
(13000704,-234375)
(16588800,529)
(40310784,-8984375)
#
# S = {2, 3, 5, 29}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(3,-3)
(3,-2)
(3,1)
(4,-3)
(5,-5)
(5,-4)
(5,-1)
(5,4)
(6,-6)
(6,-5)
(6,-2)
(6,3)
(8,1)
(9,-8)
(9,-5)
(10,-10)
(10,-9)
(10,-6)
(10,-1)
(10,6)
(12,-3)
(15,-15)
(15,-6)
(15,1)
(15,10)
(16,-15)
(16,9)
(18,-2)
(20,5)
(24,-15)
(24,1)
(25,-24)
(25,-16)
(25,-9)
(25,24)
(27,-2)
(29,-29)
(29,-25)
(29,-20)
(29,-4)
(29,20)
(30,-30)
(30,-29)
(30,-5)
(30,6)
(40,-15)
(40,9)
(45,-29)
(45,-20)
(45,4)
(48,1)
(50,-1)
(54,-50)
(54,-29)
(54,-5)
(54,10)
(58,-58)
(58,-54)
(58,-9)
(58,6)
(64,-15)
(75,6)
(80,1)
(81,-80)
(81,-32)
(81,40)
(87,-87)
(87,-6)
(90,10)
(96,-87)
(96,-15)
(96,25)
(116,5)
(120,1)
(125,-116)
(125,-4)
(144,25)
(145,-145)
(145,-144)
(145,-120)
(145,-96)
(145,-81)
(145,-64)
(145,-45)
(145,-24)
(145,-1)
(145,24)
(145,80)
(145,144)
(150,-29)
(150,-6)
(160,-135)
(160,9)
(174,-174)
(174,-125)
(174,-30)
(174,-5)
(174,150)
(216,145)
(225,-29)
(225,64)
(240,-15)
(250,-81)
(250,-54)
(250,6)
(256,-135)
(256,-87)
(261,-5)
(261,100)
(288,1)
(290,-290)
(290,-1)
(360,1)
(384,-375)
(384,145)
(405,-116)
(405,-5)
(435,-435)
(435,6)
(480,145)
(486,-290)
(486,-125)
(486,-2)
(500,29)
(580,45)
(580,261)
(625,-576)
(625,-96)
(625,216)
(625,464)
(640,-15)
(675,1)
(696,145)
(725,4)
(725,116)
(729,-725)
(729,-200)
(729,232)
(729,640)
(750,-174)
(783,1)
(783,58)
(841,-720)
(841,-480)
(841,-400)
(841,-216)
(841,120)
(841,384)
(870,-870)
(870,-29)
(870,30)
(928,-87)
(960,1)
(1080,145)
(1215,10)
(1305,-1280)
(1305,-464)
(1305,-80)
(1305,64)
(1450,-81)
(1450,-6)
(1450,486)
(1536,-15)
(1536,145)
(1566,-725)
(1600,81)
(1682,-1)
(2025,-1856)
(2320,81)
(2349,-500)
(2400,1)
(2430,-29)
(2784,25)
(2880,145)
(2880,841)
(3364,1125)
(3456,25)
(3480,1)
(3625,-3456)
(3625,-2784)
(3625,-1944)
(3625,-1024)
(3625,-261)
(3625,-144)
(3625,96)
(3625,864)
(3625,2304)
(3645,580)
(3712,9)
(3750,-29)
(4096,-375)
(4205,20)
(4350,6)
(4374,-4205)
(4374,250)
(5046,-3750)
(5046,-5)
(5184,145)
(5400,841)
(6144,-2175)
(6250,-9)
(6264,625)
(6561,-320)
(7424,145)
(7776,145)
(8410,-6561)
(8410,54)
(10240,-1215)
(11745,1024)
(11745,9280)
(15625,-11136)
(15625,-4176)
(15625,1536)
(16384,1305)
(20880,145)
(21025,-20736)
(21025,-576)
(21141,-116)
(25920,1)
(37120,6561)
(37584,3625)
(46080,145)
(48000,841)
(58000,81)
(64000,9)
(68121,-5120)
(78125,-841)
(83520,1)
(90625,-24576)
(90625,-11664)
(90625,-24)
(90625,11136)
(105705,-80)
(121945,-9720)
(121945,-1536)
(121945,-144)
(121945,55296)
(121945,103680)
(157464,145)
(210250,-486)
(219501,-78125)
(253125,-116)
(267264,25)
(393216,-315375)
(393216,-87)
(497664,90625)
(525625,11664)
(528525,4)
(531441,-11600)
(707281,-540000)
(726624,390625)
(815625,-7424)
(906250,54)
(1141614,-3125)
(1966080,121945)
(2265625,17496)
(2343750,146334)
(6291456,3625)
(8562105,-1900544)
(14432256,145)
(28697814,-1051250)
(56640625,-225504)
(102555745,384)
#
# S = {2, 3, 5, 31}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(3,-3)
(3,-2)
(3,1)
(4,-3)
(5,-5)
(5,-4)
(5,-1)
(5,4)
(6,-6)
(6,-5)
(6,-2)
(6,3)
(8,1)
(9,-8)
(9,-5)
(10,-10)
(10,-9)
(10,-6)
(10,-1)
(10,6)
(12,-3)
(15,-15)
(15,-6)
(15,1)
(15,10)
(16,-15)
(16,9)
(18,-2)
(20,5)
(24,-15)
(24,1)
(25,-24)
(25,-16)
(25,-9)
(25,24)
(27,-2)
(30,-30)
(30,-5)
(30,6)
(31,-31)
(31,-30)
(31,-27)
(31,-15)
(31,-6)
(31,5)
(31,18)
(32,-31)
(40,-31)
(40,-15)
(40,9)
(45,-20)
(45,4)
(48,1)
(50,-1)
(50,31)
(54,-50)
(54,-5)
(54,10)
(62,-62)
(62,2)
(64,-15)
(75,6)
(80,-31)
(80,1)
(81,-80)
(81,-32)
(81,40)
(90,10)
(90,31)
(93,-93)
(93,-12)
(96,-15)
(96,25)
(120,1)
(124,-75)
(124,-3)
(124,45)
(125,-124)
(125,-4)
(144,25)
(150,-6)
(155,-155)
(160,-135)
(160,9)
(162,-62)
(180,-155)
(186,-186)
(186,-150)
(186,10)
(200,-31)
(225,31)
(225,64)
(240,-15)
(250,-186)
(250,-81)
(250,-54)
(250,6)
(256,-135)
(256,-31)
(279,10)
(279,250)
(288,1)
(310,-310)
(310,-54)
(310,90)
(320,-31)
(324,-155)
(360,1)
(384,-375)
(400,-279)
(405,-5)
(405,124)
(465,-465)
(465,-384)
(465,-240)
(465,-24)
(465,64)
(465,160)
(486,-125)
(486,-2)
(496,-375)
(496,-135)
(496,465)
(620,5)
(625,-576)
(625,-96)
(625,216)
(640,-279)
(640,-15)
(675,1)
(729,-200)
(729,496)
(729,640)
(744,-15)
(744,625)
(775,-486)
(775,9)
(775,186)
(810,31)
(837,4)
(837,124)
(930,-930)
(930,-30)
(930,31)
(960,1)
(961,-960)
(961,-600)
(961,-432)
(961,-120)
(961,128)
(961,720)
(992,-31)
(1116,-155)
(1125,31)
(1215,10)
(1240,-1215)
(1240,-279)
(1240,-15)
(1250,-961)
(1440,961)
(1536,-15)
(1600,81)
(1984,-135)
(1984,225)
(2400,1)
(2511,-1550)
(2511,625)
(2560,-2511)
(2560,465)
(2976,-375)
(3125,124)
(3456,25)
(3645,-620)
(3720,1)
(3844,125)
(3875,-31)
(3968,1)
(4000,-279)
(4000,-31)
(4096,-375)
(4185,40)
(4185,4096)
(4374,250)
(4464,25)
(4960,81)
(5766,10)
(6250,-5766)
(6250,-9)
(6561,-6200)
(6561,-320)
(7750,-6)
(7936,-6975)
(7936,-15)
(9610,-6)
(9610,7290)
(10240,-1215)
(11625,-2976)
(11625,256)
(12800,-31)
(14415,-15)
(15066,310)
(15066,6250)
(15376,-1215)
(15625,-11904)
(15625,-496)
(15625,1536)
(16000,8649)
(16200,961)
(16384,-6975)
(19375,-54)
(19840,4185)
(20480,-31)
(23064,-9375)
(24025,-13824)
(25000,-22599)
(25920,1)
(29791,-21870)
(29791,-6075)
(29791,2250)
(31744,-30375)
(32000,-29791)
(36450,31)
(49600,-2511)
(50625,31744)
(59049,4960)
(62000,1)
(64000,9)
(79360,729)
(116250,31)
(119040,-15)
(126976,-98415)
(188325,31)
(203391,10)
(230400,961)
(241056,25)
(338985,7936)
(507904,-234375)
(507904,465)
(655360,-129735)
(744775,-6)
(923521,-3840)
(2460160,-10935)
(2531250,31)
(2621440,-279)
(3047424,-9375)
(3690240,1)
(3906250,-1674)
(7265625,-6291456)
(7626496,-3375)
(10983114,19375)
(15500000,-31)
(28629151,4050)
(79360000,-203391)
(130305834,156250)