# 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,
# where S = {2, 3, 5, 7, 11}.
# It contains 1418 pairs (x,y).
# Format: "(x,y)".
# Computing this list took 4042 seconds.
# Authors: Rafael von Känel and Benjamin Matschke, 2015.
# License: Creative commons 3.0 by-nc.
#
(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)
(11,-11)
(11,-10)
(11,-7)
(11,-2)
(11,5)
(12,-11)
(12,-3)
(14,-14)
(14,-10)
(14,-5)
(14,2)
(14,11)
(15,-15)
(15,-14)
(15,-11)
(15,-6)
(15,1)
(15,10)
(16,-15)
(16,-7)
(16,9)
(18,-14)
(18,-2)
(18,7)
(20,-11)
(20,5)
(21,-21)
(21,-20)
(21,-12)
(21,-5)
(21,4)
(21,15)
(22,-22)
(22,-21)
(22,-18)
(22,-6)
(22,3)
(22,14)
(24,-15)
(24,1)
(25,-24)
(25,-21)
(25,-16)
(25,-9)
(25,11)
(25,24)
(27,-11)
(27,-2)
(27,22)
(28,-27)
(28,-3)
(28,21)
(30,-30)
(30,-21)
(30,-14)
(30,-5)
(30,6)
(32,-7)
(33,-33)
(33,-32)
(33,-24)
(33,-8)
(33,3)
(33,16)
(35,-35)
(35,-10)
(35,1)
(35,14)
(36,-35)
(36,-11)
(40,-15)
(40,9)
(42,-42)
(42,-33)
(42,-6)
(42,7)
(42,22)
(44,-35)
(44,5)
(45,-44)
(45,-20)
(45,4)
(48,1)
(48,33)
(49,-48)
(49,-45)
(49,-40)
(49,-33)
(49,-24)
(49,15)
(49,32)
(50,-49)
(50,-14)
(50,-1)
(50,14)
(54,-50)
(54,-5)
(54,10)
(55,-55)
(55,-54)
(55,-30)
(55,-6)
(55,9)
(55,45)
(56,-55)
(56,-7)
(56,25)
(60,-35)
(60,-11)
(60,21)
(63,-14)
(63,1)
(64,-63)
(64,-55)
(64,-15)
(66,-66)
(66,-50)
(66,-30)
(66,-2)
(66,15)
(66,55)
(70,-70)
(70,-66)
(70,-54)
(70,-45)
(70,-21)
(70,-6)
(70,11)
(70,30)
(72,49)
(75,-66)
(75,-11)
(75,6)
(77,-77)
(77,-28)
(77,4)
(77,44)
(80,-55)
(80,1)
(81,-80)
(81,-77)
(81,-56)
(81,-32)
(81,40)
(84,-75)
(84,-35)
(84,-3)
(88,-63)
(88,-7)
(88,33)
(88,81)
(90,10)
(96,-15)
(96,25)
(98,2)
(99,-98)
(99,-50)
(99,-35)
(99,1)
(99,22)
(99,70)
(100,-99)
(100,21)
(105,-105)
(105,-96)
(105,-80)
(105,-56)
(105,-24)
(105,-5)
(105,16)
(105,64)
(110,-110)
(110,-10)
(110,11)
(112,-63)
(112,9)
(120,1)
(120,49)
(120,105)
(121,-120)
(121,-112)
(121,-105)
(121,-96)
(121,-72)
(121,-40)
(121,-21)
(121,48)
(121,75)
(125,-121)
(125,-44)
(125,-4)
(125,44)
(126,-125)
(126,-110)
(126,-77)
(126,-5)
(126,70)
(128,-7)
(132,-11)
(135,-110)
(135,-35)
(135,-14)
(135,121)
(144,25)
(147,-66)
(147,-3)
(147,22)
(150,-6)
(154,-154)
(154,-150)
(154,-105)
(154,-90)
(154,-54)
(154,-33)
(154,-10)
(154,15)
(154,42)
(154,135)
(160,-135)
(160,9)
(162,-98)
(162,7)
(165,-165)
(165,-140)
(165,-84)
(165,-44)
(165,-21)
(165,4)
(165,60)
(168,1)
(168,121)
(175,-126)
(175,-54)
(175,-6)
(175,21)
(175,81)
(176,-175)
(176,-55)
(176,-7)
(176,49)
(180,-11)
(189,-140)
(189,-125)
(189,-20)
(189,7)
(189,100)
(192,33)
(196,-75)
(196,-27)
(196,165)
(198,-98)
(198,-77)
(198,-2)
(210,-210)
(210,-110)
(210,-66)
(210,-14)
(210,15)
(220,-99)
(220,5)
(224,-175)
(224,-55)
(224,1)
(225,-224)
(225,-176)
(225,-56)
(225,64)
(231,-231)
(231,-150)
(231,-110)
(231,-35)
(231,-6)
(231,25)
(231,210)
(240,-231)
(240,-15)
(240,49)
(240,121)
(242,-98)
(242,14)
(243,-242)
(245,-220)
(245,-20)
(245,11)
(245,44)
(250,-81)
(250,-54)
(250,6)
(256,-231)
(256,-175)
(256,-135)
(256,33)
(256,105)
(264,25)
(270,-245)
(270,-14)
(275,-154)
(275,14)
(275,49)
(280,-231)
(280,-55)
(280,9)
(280,81)
(288,1)
(294,-150)
(294,-125)
(294,-5)
(294,30)
(297,-176)
(297,-128)
(297,-8)
(297,64)
(300,-11)
(320,121)
(324,-275)
(324,-35)
(330,-330)
(330,-294)
(330,-105)
(330,-6)
(330,70)
(330,154)
(336,25)
(336,105)
(343,-243)
(343,-54)
(343,18)
(350,-154)
(350,11)
(352,-343)
(352,-231)
(352,-63)
(352,9)
(360,1)
(363,-2)
(375,-294)
(375,-231)
(375,-14)
(375,66)
(375,154)
(378,22)
(384,-375)
(385,-385)
(385,-384)
(385,-360)
(385,-336)
(385,-264)
(385,-216)
(385,-189)
(385,-160)
(385,-96)
(385,-24)
(385,15)
(385,56)
(385,99)
(385,144)
(385,240)
(396,-275)
(396,-35)
(400,-231)
(405,-44)
(405,-5)
(405,220)
(420,21)
(440,1)
(441,-440)
(441,-320)
(441,-80)
(441,88)
(441,400)
(448,-7)
(448,81)
(462,-462)
(462,-21)
(462,22)
(480,49)
(484,-315)
(484,45)
(484,245)
(486,-125)
(486,-2)
(490,-486)
(490,-90)
(490,-6)
(490,135)
(495,-11)
(504,25)
(504,121)
(512,-343)
(525,-84)
(525,4)
(528,1)
(539,-250)
(539,-55)
(539,-10)
(540,-539)
(540,-11)
(550,-486)
(550,-294)
(550,-189)
(550,-66)
(550,-21)
(550,126)
(550,539)
(576,49)
(576,385)
(588,-363)
(594,-110)
(605,20)
(616,-567)
(616,-495)
(616,-175)
(616,9)
(616,225)
(625,-616)
(625,-576)
(625,-504)
(625,-336)
(625,-264)
(625,-96)
(625,-49)
(625,216)
(625,336)
(630,-605)
(630,-5)
(630,154)
(640,-15)
(660,-539)
(660,-35)
(672,-231)
(675,1)
(686,-605)
(686,-110)
(686,-10)
(686,275)
(704,-343)
(704,-175)
(704,25)
(704,385)
(720,121)
(726,-150)
(726,-50)
(726,3)
(729,-704)
(729,-560)
(729,-440)
(729,-245)
(729,-200)
(729,55)
(729,112)
(729,640)
(735,-726)
(735,-110)
(735,-6)
(735,165)
(750,-686)
(750,-21)
(770,-770)
(770,14)
(784,-495)
(784,-55)
(792,49)
(825,-704)
(825,-384)
(825,-96)
(825,16)
(825,264)
(840,1)
(840,121)
(840,385)
(847,-486)
(847,-63)
(847,-6)
(847,378)
(880,81)
(891,-875)
(891,-770)
(891,-50)
(891,70)
(896,-847)
(896,-55)
(896,625)
(900,-539)
(924,-875)
(924,165)
(945,-896)
(945,-320)
(945,16)
(945,280)
(960,-735)
(960,-231)
(960,1)
(968,-343)
(968,-7)
(972,-11)
(1024,-735)
(1024,-495)
(1024,-63)
(1024,825)
(1029,-500)
(1029,-300)
(1029,-5)
(1029,60)
(1050,-726)
(1056,33)
(1056,625)
(1078,-594)
(1078,-54)
(1078,11)
(1089,-800)
(1089,-560)
(1089,-128)
(1089,280)
(1100,-11)
(1120,-495)
(1120,105)
(1120,729)
(1120,1089)
(1134,-605)
(1134,-350)
(1134,-110)
(1134,22)
(1155,-1155)
(1155,-66)
(1155,1)
(1155,70)
(1210,-810)
(1210,-54)
(1210,15)
(1215,-686)
(1215,-539)
(1215,10)
(1215,154)
(1215,385)
(1225,-1056)
(1225,-864)
(1225,-384)
(1225,-264)
(1225,144)
(1225,891)
(1232,-7)
(1250,686)
(1260,-35)
(1280,-55)
(1296,385)
(1320,-231)
(1320,49)
(1323,121)
(1331,-1250)
(1331,-490)
(1331,-175)
(1331,-35)
(1331,350)
(1344,25)
(1372,-3)
(1375,-891)
(1375,-6)
(1386,550)
(1400,121)
(1408,-567)
(1408,441)
(1458,-14)
(1485,196)
(1500,-1331)
(1500,-539)
(1500,21)
(1536,-15)
(1540,-315)
(1540,1485)
(1584,625)
(1584,1225)
(1600,-231)
(1600,81)
(1617,-1536)
(1617,-528)
(1617,-96)
(1617,64)
(1617,1408)
(1620,-1331)
(1680,1)
(1694,-250)
(1694,70)
(1701,-20)
(1701,700)
(1728,121)
(1750,-1701)
(1750,-726)
(1750,-594)
(1750,14)
(1750,99)
(1750,1386)
(1782,154)
(1792,-567)
(1800,49)
(1815,-1715)
(1815,-294)
(1815,210)
(1848,1)
(1875,726)
(1890,-1694)
(1920,105)
(1925,11)
(1936,-1575)
(1936,-567)
(2016,385)
(2025,-176)
(2025,784)
(2058,-33)
(2079,625)
(2160,49)
(2187,22)
(2200,-2079)
(2200,9)
(2205,-605)
(2205,4)
(2310,-2310)
(2310,-6)
(2376,25)
(2400,1)
(2401,-2400)
(2401,-2376)
(2401,-2112)
(2401,-1440)
(2401,-880)
(2401,-720)
(2401,-192)
(2401,99)
(2401,200)
(2401,1080)
(2401,1320)
(2430,70)
(2464,-1375)
(2464,-63)
(2464,2025)
(2475,-539)
(2500,-99)
(2541,-2100)
(2541,-140)
(2541,60)
(2541,375)
(2541,2500)
(2625,-1536)
(2625,-224)
(2625,-24)
(2625,1344)
(2640,385)
(2640,2401)
(2662,-2646)
(2662,-1701)
(2662,-162)
(2662,42)
(2662,147)
(2673,-2048)
(2673,352)
(2688,121)
(2695,-486)
(2695,9)
(2695,330)
(2700,-1331)
(2744,-1375)
(2800,9)
(2816,-2695)
(2816,-7)
(2970,55)
(3024,1)
(3025,-3024)
(3025,-1344)
(3025,-1176)
(3025,-216)
(3025,224)
(3025,2016)
(3025,2304)
(3080,-55)
(3125,11)
(3136,1089)
(3150,-14)
(3200,49)
(3234,-2750)
(3234,15)
(3360,121)
(3375,-1694)
(3375,-11)
(3375,2401)
(3430,-726)
(3430,-405)
(3430,-66)
(3430,1331)
(3430,2970)
(3456,25)
(3465,-2240)
(3465,-440)
(3465,16)
(3465,256)
(3465,1024)
(3465,2464)
(3520,-495)
(3564,-1715)
(3564,-539)
(3584,-1375)
(3584,385)
(3600,121)
(3630,-1029)
(3630,-30)
(3645,-2420)
(3696,25)
(3840,-1815)
(3840,385)
(3840,2401)
(3850,-486)
(3850,-6)
(3850,2079)
(3969,-1760)
(3969,-605)
(3969,-125)
(3969,256)
(3993,-512)
(3993,-24)
(3993,768)
(4050,-686)
(4096,-847)
(4096,-375)
(4096,945)
(4125,-4116)
(4125,231)
(4200,-231)
(4224,1)
(4235,-10)
(4312,729)
(4356,-875)
(4374,250)
(4375,-4374)
(4480,-4455)
(4480,-2079)
(4480,9)
(4500,-11)
(4704,625)
(4851,625)
(4860,-4235)
(5040,1)
(5145,-5120)
(5145,-384)
(5145,480)
(5250,-66)
(5280,49)
(5324,5)
(5346,-1250)
(5544,385)
(5625,-2816)
(5625,616)
(5632,-5103)
(5632,-7)
(5632,297)
(5670,-770)
(5775,1)
(5775,154)
(5929,-5760)
(5929,-5400)
(5929,-1440)
(5929,-600)
(5929,960)
(5929,1296)
(5940,-1715)
(5940,-11)
(6125,5324)
(6160,-231)
(6160,81)
(6160,729)
(6174,550)
(6174,2662)
(6237,-308)
(6237,4)
(6250,-9)
(6561,-6272)
(6561,-5600)
(6561,-3080)
(6561,-1232)
(6561,-320)
(6561,2464)
(6655,-2430)
(6776,-4375)
(6804,-875)
(6875,14)
(7203,22)
(7260,-35)
(7546,-7425)
(7546,-7290)
(7546,-6250)
(7546,-150)
(7546,198)
(7546,375)
(7744,-175)
(7840,81)
(7920,1)
(8019,-275)
(8019,-98)
(8019,3430)
(8085,15)
(8316,-35)
(8470,-4374)
(8470,-189)
(8470,-6)
(8470,1134)
(8505,-1280)
(8505,-224)
(8624,25)
(8640,385)
(8750,-1694)
(8800,3969)
(9375,-726)
(9375,-539)
(9375,1029)
(9408,1)
(9450,154)
(9604,-9075)
(9625,-9504)
(9625,-7776)
(9625,-6144)
(9625,-3696)
(9625,-1344)
(9625,-216)
(9625,-21)
(9625,176)
(9625,576)
(9625,4536)
(9625,8064)
(9800,1)
(9801,-9800)
(9801,-8960)
(9801,-392)
(9801,400)
(9856,-1575)
(9856,-55)
(9856,2025)
(10000,-2079)
(10080,121)
(10125,484)
(10206,-1925)
(10206,-5)
(10240,-1215)
(10290,-7986)
(10368,2401)
(10560,49)
(10584,25)
(10935,-1331)
(11025,7744)
(11250,-14)
(11264,-4375)
(11319,-3750)
(11760,121)
(11880,1)
(11979,-98)
(12288,33)
(12320,1)
(12474,70)
(12544,-12375)
(12544,225)
(12705,-6144)
(12705,-1680)
(12705,-384)
(12705,64)
(13230,-5)
(13365,-140)
(13720,-495)
(13750,-9261)
(13750,-294)
(13750,891)
(13750,1134)
(14080,81)
(14175,-14)
(14256,385)
(14336,-175)
(14406,-6)
(14553,88)
(14641,-14112)
(14641,-12960)
(14641,-9600)
(14641,-8400)
(14641,-6720)
(14641,-4032)
(14641,-480)
(14641,243)
(14641,735)
(14641,2000)
(14641,2520)
(14641,3584)
(14641,7560)
(15125,4)
(15309,-12500)
(15360,-231)
(15400,729)
(15625,-14784)
(15625,-14256)
(15625,-10584)
(15625,-1936)
(15625,-1701)
(15625,504)
(15625,1536)
(15625,3696)
(15625,12936)
(15680,-6655)
(15680,-55)
(16038,-4802)
(16128,1)
(16335,49)
(16384,-16335)
(16384,-14175)
(16384,-5775)
(16384,-2695)
(16807,13122)
(17010,-110)
(17150,11)
(17500,189)
(17920,-231)
(17920,12705)
(18144,625)
(18225,-6776)
(18225,-3584)
(18375,121)
(18634,-3750)
(18634,-2250)
(18634,-945)
(18634,135)
(18750,294)
(18865,-17496)
(18865,-15840)
(18865,-13824)
(18865,-4224)
(18865,-3240)
(18865,-640)
(18865,-96)
(18865,1584)
(18865,2160)
(18865,15360)
(19200,121)
(19360,6561)
(19602,-2)
(19800,2401)
(19965,-84)
(20625,-176)
(20736,18865)
(21120,-11319)
(21175,729)
(21296,-16807)
(21504,105)
(21609,-11000)
(22000,6561)
(22176,25)
(22176,625)
(22528,-2079)
(22680,121)
(23625,1024)
(24000,5929)
(24010,15)
(24057,-32)
(24640,-18711)
(24640,9)
(25344,1225)
(25344,9625)
(25600,-18711)
(25920,1)
(26244,-13475)
(26250,-6)
(26950,-54)
(26950,8019)
(27500,-26411)
(28000,-27951)
(28000,-2079)
(28125,-5324)
(28512,49)
(30240,385)
(30618,7)
(30625,-26136)
(30625,704)
(30976,-3087)
(31185,-28160)
(31185,-560)
(32076,-21875)
(32076,-35)
(32670,3430)
(32768,-7)
(32805,-44)
(33614,-30250)
(33614,-125)
(33614,242)
(34375,594)
(34496,-34375)
(34848,2401)
(35200,-231)
(35721,-32000)
(35721,8800)
(36864,385)
(37125,-2156)
(37800,14641)
(38808,1)
(39424,-39375)
(39424,-4455)
(39600,1)
(39930,70)
(40425,-24)
(40425,4096)
(40824,385)
(42592,-567)
(43120,-40095)
(43659,22)
(43740,-1715)
(43750,-2541)
(43750,-486)
(43904,-6655)
(45056,-8575)
(45056,-1375)
(45375,-6)
(46305,-80)
(46464,625)
(46585,-45360)
(46585,-40960)
(46585,-13824)
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