# 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, p},
# where p ranges over all other primes less or equal to 250.
# It contains 238 pairs (x,y), some of which may appear for more than one S.
# Format: "(x,y)".
# Computing this list took 558 seconds.
# Authors: Rafael von Känel and Benjamin Matschke, 2015.
# License: Creative commons 3.0 by-nc.
#
#
# S = {2, 3}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(3,-3)
(3,-2)
(3,1)
(4,-3)
(6,-6)
(6,-2)
(6,3)
(8,1)
(9,-8)
(12,-3)
(16,9)
(18,-2)
(24,1)
(27,-2)
(48,1)
(81,-32)
(288,1)
(486,-2)
#
# S = {2, 5}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(5,-5)
(5,-4)
(5,-1)
(5,4)
(8,1)
(10,-10)
(10,-1)
(20,5)
(25,-16)
(50,-1)
(80,1)
(125,-4)
#
# S = {2, 7}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(7,-7)
(7,2)
(8,-7)
(8,1)
(14,-14)
(14,2)
(16,-7)
(32,-7)
(49,32)
(56,-7)
(98,2)
(128,-7)
(224,1)
(448,-7)
(512,-343)
(32768,-7)
#
# S = {2, 11}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(11,-11)
(11,-2)
(22,-22)
#
# S = {2, 13}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(13,-13)
(13,-4)
(26,-26)
(26,-1)
(57122,-1)
#
# S = {2, 17}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(17,-17)
(17,-16)
(17,-8)
(17,-1)
(17,8)
(32,17)
(34,-34)
(34,2)
(64,17)
(272,17)
(289,-64)
(512,17)
(578,-2)
(1088,1)
(4913,128)
#
# S = {2, 19}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(19,-19)
(38,-38)
(38,-2)
#
# S = {2, 23}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(23,-23)
(23,2)
(32,-23)
(46,-46)
(2048,-23)
(24334,2)
#
# S = {2, 29}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(29,-29)
(29,-4)
(58,-58)
(1682,-1)
#
# S = {2, 31}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(31,-31)
(32,-31)
(62,-62)
(62,2)
(256,-31)
(961,128)
(992,-31)
(3968,1)
#
# S = {2, 37}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(37,-37)
(37,-1)
(74,-74)
#
# S = {2, 41}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(41,-41)
(41,-32)
(41,-16)
(41,8)
(82,-82)
(82,-1)
(128,41)
(3362,2)
(41984,41)
#
# S = {2, 43}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(43,-43)
(86,-86)
#
# S = {2, 47}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(47,-47)
(47,2)
(94,-94)
(128,-47)
#
# S = {2, 53}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(53,-53)
(53,-4)
(106,-106)
#
# S = {2, 59}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(59,-59)
(118,-118)
#
# S = {2, 61}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(61,-61)
(122,-122)
(122,-1)
#
# S = {2, 67}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(67,-67)
(134,-134)
#
# S = {2, 71}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(71,-71)
(142,-142)
(142,2)
(512,-71)
#
# S = {2, 73}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(73,-73)
(73,-64)
(73,8)
(146,-146)
(146,-2)
#
# S = {2, 79}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(79,-79)
(79,2)
(128,-79)
(158,-158)
#
# S = {2, 83}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(83,-83)
(83,-2)
(166,-166)
#
# S = {2, 89}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(89,-89)
(89,-64)
(89,-8)
(89,32)
(178,-178)
(8192,89)
#
# S = {2, 97}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(97,-97)
(97,-16)
(128,97)
(194,-194)
(194,2)
#
# S = {2, 101}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(101,-101)
(101,-1)
(202,-202)
#
# S = {2, 103}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(103,-103)
(128,-103)
(206,-206)
#
# S = {2, 107}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(107,-107)
(214,-214)
#
# S = {2, 109}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(109,-109)
(218,-218)
#
# S = {2, 113}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(113,-113)
(113,-64)
(113,-32)
(113,8)
(226,-226)
(226,-1)
(512,113)
#
# S = {2, 127}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(127,-127)
(128,-127)
(254,-254)
(254,2)
(4096,-127)
(16129,512)
(16256,-127)
(65024,1)
#
# S = {2, 131}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(131,-131)
(262,-262)
#
# S = {2, 137}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(137,-137)
(137,-128)
(137,-16)
(137,32)
(274,-274)
#
# S = {2, 139}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(139,-139)
(278,-278)
#
# S = {2, 149}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(149,-149)
(298,-298)
#
# S = {2, 151}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(151,-151)
(302,-302)
(512,-151)
#
# S = {2, 157}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(157,-157)
(314,-314)
#
# S = {2, 163}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(163,-163)
(326,-326)
(326,-2)
#
# S = {2, 167}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(167,-167)
(167,2)
(334,-334)
#
# S = {2, 173}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(173,-173)
(173,-4)
(346,-346)
#
# S = {2, 179}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(179,-179)
(358,-358)
#
# S = {2, 181}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(181,-181)
(362,-362)
(362,-1)
#
# S = {2, 191}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(191,-191)
(382,-382)
#
# S = {2, 193}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(193,-193)
(193,32)
(386,-386)
#
# S = {2, 197}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(197,-197)
(197,-1)
(394,-394)
#
# S = {2, 199}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(199,-199)
(398,-398)
(398,2)
(2048,-199)
#
# S = {2, 211}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(211,-211)
(422,-422)
#
# S = {2, 223}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(223,-223)
(223,2)
(446,-446)
(512,-223)
#
# S = {2, 227}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(227,-227)
(227,-2)
(454,-454)
#
# S = {2, 229}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(229,-229)
(229,-4)
(458,-458)
#
# S = {2, 233}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(233,-233)
(233,-64)
(233,-8)
(233,128)
(466,-466)
#
# S = {2, 239}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(239,-239)
(478,-478)
(114242,2)
#
# S = {2, 241}:
#
(1,-1)
(2,-2)
(2,-1)
(2,2)
(8,1)
(241,-241)
(241,-16)
(482,-482)
(482,2)