# List of all pairs of integers (x,y) such that
# x + y is a cube, gcd(x,y) is cube-free, x >= y, |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 372 pairs (x,y), some of which may appear for more than one S.
# Format: "(x,y)".
# Computing this list took 976 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)
(3,-3)
(3,-2)
(4,-4)
(4,-3)
(4,4)
(6,-6)
(6,2)
(9,-9)
(9,-8)
(9,-1)
(12,-12)
(12,-4)
(18,-18)
(18,9)
(24,3)
(36,-36)
(36,-9)
(128,-3)
#
# S = {2, 5}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(5,-5)
(5,-4)
(10,-10)
(10,-2)
(20,-20)
(25,-25)
(25,2)
(32,-5)
(50,-50)
(100,-100)
(100,25)
#
# S = {2, 7}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(7,-7)
(7,1)
(8,-7)
(14,-14)
(28,-28)
(28,-1)
(49,-49)
(98,-98)
(196,-196)
(392,-49)
#
# S = {2, 11}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(11,-11)
(16,11)
(22,-22)
(44,-44)
(121,-121)
(121,4)
(242,-242)
(484,-484)
#
# S = {2, 13}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(13,-13)
(26,-26)
(26,1)
(52,-52)
(169,-169)
(338,-338)
(512,-169)
(676,-676)
#
# S = {2, 17}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(17,-17)
(17,-16)
(34,-34)
(68,-68)
(68,-4)
(289,-289)
(578,-578)
(1156,-1156)
(4624,289)
#
# S = {2, 19}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(19,-19)
(19,8)
(38,-38)
(76,-76)
(361,-361)
(722,-722)
(1444,-1444)
(184832,361)
#
# S = {2, 23}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(23,-23)
(23,4)
(46,-46)
(92,-92)
(529,-529)
(1058,-1058)
(2116,-2116)
#
# S = {2, 29}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(29,-29)
(29,-2)
(58,-58)
(116,-116)
(841,-841)
(1682,-1682)
(3364,-3364)
#
# S = {2, 31}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(31,-31)
(31,-4)
(32,-31)
(62,-62)
(62,2)
(124,-124)
(124,1)
(961,-961)
(1922,-1922)
(3844,-3844)
(30752,-961)
#
# S = {2, 37}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(37,-37)
(64,-37)
(74,-74)
(148,-148)
(1369,-1369)
(2738,-2738)
(5476,-5476)
#
# S = {2, 41}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(41,-41)
(82,-82)
(164,-164)
(1681,-1681)
(3362,-3362)
(6724,-6724)
#
# S = {2, 43}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(43,-43)
(43,-16)
(86,-86)
(172,-172)
(344,-1)
(1849,-1849)
(3698,-3698)
(7396,-7396)
#
# S = {2, 47}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(47,-47)
(94,-94)
(188,-188)
(2209,-2209)
(4418,-4418)
(8836,-8836)
#
# S = {2, 53}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(53,-53)
(106,-106)
(212,-212)
(212,4)
(2809,-2809)
(5618,-5618)
(11236,-11236)
#
# S = {2, 59}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(59,-59)
(59,-32)
(118,-118)
(236,-236)
(3481,-3481)
(6962,-6962)
(13924,-13924)
#
# S = {2, 61}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(61,-61)
(64,61)
(122,-122)
(244,-244)
(3721,-3721)
(7442,-7442)
(14884,-14884)
#
# S = {2, 67}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(67,-67)
(134,-134)
(268,-268)
(4489,-4489)
(8978,-8978)
(17956,-17956)
#
# S = {2, 71}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(71,-71)
(142,-142)
(284,-284)
(5041,-5041)
(5041,-128)
(10082,-10082)
(20164,-20164)
#
# S = {2, 73}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(73,-73)
(146,-146)
(292,-292)
(5329,-5329)
(10658,-10658)
(21316,-21316)
#
# S = {2, 79}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(79,-79)
(158,-158)
(316,-316)
(6241,-6241)
(12482,-12482)
(24964,-24964)
#
# S = {2, 83}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(83,-83)
(166,-166)
(332,-332)
(6889,-6889)
(13778,-13778)
(27556,-27556)
#
# S = {2, 89}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(89,-89)
(178,-178)
(356,-356)
(7921,-7921)
(15842,-15842)
(31684,-31684)
#
# S = {2, 97}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(97,-97)
(194,-194)
(388,-388)
(9409,-9409)
(18818,-18818)
(37636,-37636)
#
# S = {2, 101}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(101,-101)
(128,-101)
(202,-202)
(404,-404)
(10201,-10201)
(20402,-20402)
(40804,-40804)
#
# S = {2, 103}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(103,-103)
(206,-206)
(412,-412)
(10609,-10609)
(21218,-21218)
(42436,-42436)
#
# S = {2, 107}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(107,-107)
(214,-214)
(214,2)
(428,-428)
(11449,-11449)
(22898,-22898)
(45796,-45796)
#
# S = {2, 109}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(109,-109)
(109,16)
(218,-218)
(218,-2)
(436,-436)
(11881,-11881)
(23762,-23762)
(47524,-47524)
#
# S = {2, 113}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(113,-113)
(226,-226)
(452,-452)
(12769,-12769)
(25538,-25538)
(51076,-51076)
#
# S = {2, 127}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(127,-127)
(127,-2)
(128,-127)
(254,-254)
(508,-508)
(508,4)
(16129,-16129)
(32258,-32258)
(64516,-64516)
(2064512,-16129)
#
# S = {2, 131}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(131,-131)
(256,-131)
(262,-262)
(524,-524)
(17161,-17161)
(34322,-34322)
(68644,-68644)
#
# S = {2, 137}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(137,-137)
(274,-274)
(548,-548)
(18769,-18769)
(37538,-37538)
(75076,-75076)
#
# S = {2, 139}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(139,-139)
(278,-278)
(556,-556)
(19321,-19321)
(38642,-38642)
(77284,-77284)
#
# S = {2, 149}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(149,-149)
(298,-298)
(596,-596)
(2048,149)
(22201,-22201)
(44402,-44402)
(88804,-88804)
#
# S = {2, 151}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(151,-151)
(302,-302)
(604,-604)
(22801,-22801)
(45602,-45602)
(91204,-91204)
#
# S = {2, 157}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(157,-157)
(157,-32)
(314,-314)
(628,-628)
(24649,-24649)
(49298,-49298)
(98596,-98596)
#
# S = {2, 163}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(163,-163)
(326,-326)
(652,-652)
(26569,-26569)
(53138,-53138)
(106276,-106276)
#
# S = {2, 167}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(167,-167)
(334,-334)
(668,-668)
(27889,-27889)
(55778,-55778)
(111556,-111556)
#
# S = {2, 173}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(173,-173)
(346,-346)
(692,-692)
(29929,-29929)
(59858,-59858)
(119716,-119716)
#
# S = {2, 179}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(179,-179)
(358,-358)
(716,-716)
(32041,-32041)
(64082,-64082)
(128164,-128164)
#
# S = {2, 181}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(181,-181)
(362,-362)
(724,-724)
(32761,-32761)
(65522,-65522)
(131044,-131044)
#
# S = {2, 191}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(191,-191)
(382,-382)
(764,-764)
(36481,-36481)
(72962,-72962)
(145924,-145924)
#
# S = {2, 193}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(193,-193)
(386,-386)
(772,-772)
(37249,-37249)
(74498,-74498)
(148996,-148996)
#
# S = {2, 197}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(197,-197)
(394,-394)
(788,-788)
(38809,-38809)
(77618,-77618)
(155236,-155236)
#
# S = {2, 199}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(199,-199)
(398,-398)
(796,-796)
(39601,-39601)
(79202,-79202)
(158404,-158404)
#
# S = {2, 211}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(211,-211)
(422,-422)
(844,-844)
(3376,-1)
(44521,-44521)
(89042,-89042)
(178084,-178084)
#
# S = {2, 223}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(223,-223)
(446,-446)
(892,-892)
(49729,-49729)
(99458,-99458)
(198916,-198916)
#
# S = {2, 227}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(227,-227)
(454,-454)
(908,-908)
(51529,-51529)
(103058,-103058)
(206116,-206116)
#
# S = {2, 229}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(229,-229)
(256,-229)
(458,-458)
(916,-916)
(52441,-52441)
(104882,-104882)
(209764,-209764)
#
# S = {2, 233}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(233,-233)
(466,-466)
(932,-932)
(54289,-54289)
(108578,-108578)
(217156,-217156)
#
# S = {2, 239}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(239,-239)
(478,-478)
(956,-956)
(57121,-57121)
(114242,-114242)
(228484,-228484)
#
# S = {2, 241}:
#
(1,-1)
(2,-2)
(2,-1)
(4,-4)
(4,4)
(241,-241)
(482,-482)
(964,-964)
(58081,-58081)
(116162,-116162)
(232324,-232324)