# 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, 3, p}, # where p ranges over all other primes less or equal to 100. # It contains 730 pairs (x,y), some of which may appear for more than one S. # Format: "(x,y)". # Computing this list took 3675 seconds. # Authors: Rafael von Känel and Benjamin Matschke, 2015. # License: Creative commons 3.0 by-nc. # # # S = {2, 3, 5}: # (1,-1) (2,-2) (2,-1) (3,-3) (3,-2) (4,-4) (4,-3) (4,4) (5,-5) (5,-4) (5,3) (6,-6) (6,-5) (6,2) (9,-9) (9,-8) (9,-1) (10,-10) (10,-9) (10,-2) (12,-12) (12,-4) (15,-15) (15,12) (16,-15) (18,-18) (18,-10) (18,9) (20,-20) (20,-12) (24,3) (25,-25) (25,-24) (25,2) (30,-30) (30,-3) (32,-5) (36,-36) (36,-9) (45,-45) (45,-18) (50,-50) (54,10) (60,-60) (60,4) (72,-45) (75,-75) (75,-48) (75,50) (80,45) (81,-80) (90,-90) (100,-100) (100,-36) (100,25) (108,-100) (120,5) (128,-3) (135,-10) (150,-150) (150,-25) (180,-180) (180,36) (200,-75) (225,-225) (225,-100) (225,-9) (243,100) (300,-300) (375,-32) (450,-450) (500,12) (720,9) (800,-675) (900,-900) (900,100) (1152,-1125) (1250,81) (2187,10) (3600,-225) (8100,-100) (9216,45) # # S = {2, 3, 7}: # (1,-1) (2,-2) (2,-1) (3,-3) (3,-2) (4,-4) (4,-3) (4,4) (6,-6) (6,2) (7,-7) (7,-6) (7,1) (8,-7) (9,-9) (9,-8) (9,-1) (12,-12) (12,-4) (14,-14) (14,-6) (18,-18) (18,9) (21,-21) (21,6) (24,3) (28,-28) (28,-27) (28,-1) (36,-36) (36,-28) (36,-9) (36,28) (42,-42) (48,-21) (49,-49) (49,-48) (63,-63) (63,-36) (63,1) (64,-63) (84,-84) (98,-98) (98,27) (126,-126) (126,-1) (128,-3) (147,-147) (162,-98) (189,-64) (196,-196) (196,147) (252,-252) (252,-36) (294,-294) (294,49) (336,7) (392,-49) (441,-441) (441,-98) (441,288) (567,-224) (588,-588) (784,-441) (882,-882) (972,28) (1323,8) (1764,-1764) (1764,-36) (2646,98) (3087,288) (9408,-147) # # S = {2, 3, 11}: # (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) (11,-11) (11,-3) (12,-12) (12,-11) (12,-4) (16,11) (18,-18) (18,9) (22,-22) (24,3) (33,-33) (33,-32) (33,-6) (36,-36) (36,-9) (44,-44) (44,-36) (66,-66) (66,-2) (81,44) (99,-99) (99,-72) (108,-44) (121,-121) (121,4) (128,-3) (132,-132) (198,-198) (198,18) (242,-242) (243,-242) (352,-9) (363,-363) (396,-396) (484,-484) (726,-726) (726,3) (968,363) (1089,-1089) (1089,242) (1452,-1452) (1452,-121) (2178,-2178) (3267,-1936) (4356,-4356) (10692,-44) (12288,-121) (34848,1089) # # S = {2, 3, 13}: # (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) (13,-13) (13,-12) (18,-18) (18,9) (24,3) (26,-26) (26,-18) (26,1) (27,-26) (36,-36) (36,-9) (39,-39) (39,-12) (52,-52) (52,12) (78,-78) (117,-117) (117,8) (128,-3) (144,-117) (156,-156) (169,-169) (234,-234) (234,-18) (338,-338) (351,-8) (468,-468) (486,26) (507,-507) (512,-169) (676,-676) (676,324) (768,-39) (1014,-1014) (1521,-1521) (1521,676) (2028,-2028) (2028,169) (2704,-507) (3042,-3042) (6084,-6084) (12168,-1) (18252,-676) (43264,-41067) # # S = {2, 3, 17}: # (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) (17,-17) (17,-16) (17,-9) (18,-18) (18,-17) (18,9) (24,3) (34,-34) (36,-36) (36,-9) (51,-51) (51,-24) (68,-68) (68,-4) (81,-17) (102,-102) (108,17) (128,-3) (153,-153) (204,-204) (204,12) (289,-289) (289,-288) (289,54) (306,-306) (576,153) (578,-578) (612,-612) (867,-867) (1088,243) (1156,-1156) (1734,-1734) (1734,-6) (2312,-2187) (2601,-2601) (2601,2312) (3468,-3468) (4624,289) (4896,17) (5202,-5202) (5202,-289) (10404,-10404) (23409,-18496) (1685448,-289) # # S = {2, 3, 19}: # (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) (19,-19) (19,-18) (19,8) (24,3) (27,-19) (36,-36) (36,-9) (38,-38) (57,-57) (76,-76) (76,-12) (114,-114) (128,-3) (144,-19) (152,-27) (171,-171) (171,-144) (228,-228) (228,-12) (324,19) (342,-342) (342,1) (361,-361) (361,-18) (486,-361) (513,-512) (513,-1) (684,-684) (722,-722) (1083,-1083) (1444,-1444) (2166,-2166) (3249,-3249) (4332,-4332) (5776,1083) (6498,-6498) (6498,361) (9747,-2888) (12996,-12996) (184832,361) # # S = {2, 3, 23}: # (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) (23,-23) (23,4) (24,-23) (24,3) (36,-36) (36,-9) (46,-46) (46,18) (54,-46) (69,-69) (92,-92) (96,-69) (128,-3) (138,-138) (207,-207) (207,9) (276,-276) (368,-243) (414,-414) (529,-529) (828,-828) (1058,-1058) (1587,-1587) (1587,-256) (2116,-2116) (2116,81) (3174,-3174) (4761,-4761) (6348,-6348) (9522,-9522) (12696,-529) (14283,-2116) (16928,-4761) (19044,-19044) # # S = {2, 3, 29}: # (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) (29,-29) (29,-2) (36,-36) (36,-9) (58,-58) (58,6) (87,-87) (96,29) (116,-116) (116,-108) (116,9) (128,-3) (174,-174) (256,87) (261,-261) (288,-261) (348,-348) (522,-522) (841,-841) (1044,-1044) (1682,-1682) (2523,-2523) (3364,-3364) (5046,-5046) (7569,-7569) (10092,-10092) (15138,-15138) (22707,1682) (26912,-2523) (30276,-30276) (59392,-59049) # # S = {2, 3, 31}: # (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) (31,-31) (31,-4) (32,-31) (36,-36) (36,-9) (62,-62) (62,-54) (62,2) (93,-93) (93,32) (124,-124) (124,1) (128,-3) (186,-186) (279,-279) (279,64) (372,-372) (558,-558) (961,-961) (1116,-1116) (1922,-1922) (2883,-2883) (3844,-3844) (5766,-5766) (8649,-8649) (11532,-11532) (17298,-17298) (25947,3844) (30752,-961) (34596,-34596) (39366,-62) # # S = {2, 3, 37}: # (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) (37,-37) (37,-36) (37,27) (64,-37) (74,-74) (111,-111) (128,-3) (148,-148) (162,-37) (222,-222) (222,-6) (333,-333) (444,-444) (666,-666) (999,1) (1332,-1332) (1332,-1) (1369,-1369) (2738,-2738) (2738,6) (4107,-4107) (5476,-5476) (8214,-8214) (12321,-12321) (16428,-16428) (24642,-24642) (49284,-49284) (49284,1369) (87616,-36963) # # S = {2, 3, 41}: # (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) (41,-41) (82,-82) (82,-81) (82,-18) (123,-123) (123,-96) (123,2) (128,-3) (164,-164) (246,-246) (369,-369) (384,-41) (492,-492) (738,-738) (738,-9) (1476,-1476) (1681,-1681) (3362,-3362) (5043,-5043) (6724,-6724) (10086,-10086) (15129,-15129) (20172,-20172) (30258,-30258) (53792,15129) (60516,-60516) (544644,6724) # # S = {2, 3, 43}: # (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) (43,-43) (43,-16) (86,-86) (128,-3) (129,-129) (129,-128) (129,-4) (172,-172) (172,-108) (258,-258) (344,-1) (387,-387) (512,-387) (516,-516) (516,-4) (774,-774) (1548,-1548) (1849,-1849) (2916,-172) (3698,-3698) (5547,-5547) (7396,-7396) (11094,-11094) (16641,-16641) (22188,-22188) (33282,-33282) (49923,29584) (66564,-66564) (2130048,16641) # # S = {2, 3, 47}: # (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) (47,-47) (48,-47) (94,-94) (128,-3) (141,-141) (141,-16) (188,-188) (282,-282) (324,188) (423,-423) (564,-564) (846,-846) (1152,-423) (1692,-1692) (1692,36) (2209,-2209) (2209,-12) (3384,-9) (4418,-4418) (6627,-6627) (8836,-8836) (13254,-13254) (19881,-19881) (26508,-26508) (39762,-39762) (79524,-79524) (106032,-2209) (282752,-178929) # # S = {2, 3, 53}: # (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) (53,-53) (54,-53) (72,53) (106,-106) (128,-3) (159,-159) (212,-212) (212,4) (318,-318) (424,-81) (477,-477) (636,-636) (954,-954) (1908,-1908) (2809,-2809) (5618,-5618) (6912,-53) (8427,-8427) (11236,-11236) (16854,-16854) (25281,-25281) (33708,-33708) (50562,-50562) (101124,-101124) (151686,-2809) (18429849,179776) # # S = {2, 3, 59}: # (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) (59,-59) (59,-32) (118,-118) (118,-54) (128,-3) (177,-177) (236,-236) (243,-118) (354,-354) (531,-531) (708,-708) (1062,-1062) (2124,-2124) (3481,-3481) (6962,-6962) (10443,-10443) (13924,-13924) (20886,-20886) (31329,-31329) (31329,4608) (41772,-41772) (62658,-62658) (111392,93987) (125316,-125316) # # S = {2, 3, 61}: # (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) (61,-61) (61,3) (64,61) (122,-122) (122,3) (128,-3) (183,-183) (244,-244) (244,-243) (366,-366) (549,-549) (576,-549) (732,-732) (732,-3) (1098,-1098) (2196,-2196) (2196,1) (3721,-3721) (7442,-7442) (11163,-11163) (14884,-14884) (15616,9) (22326,-22326) (33489,-33489) (36864,-33489) (44652,-44652) (66978,-66978) (133956,-133956) (238144,-11163) (1808406,7442) # # S = {2, 3, 67}: # (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) (67,-67) (67,-3) (128,-3) (134,-134) (134,-9) (192,-67) (201,-201) (268,-268) (402,-402) (603,-603) (603,-576) (804,-804) (1072,-729) (1206,-1206) (2412,-2412) (4489,-4489) (5427,-4096) (8978,-8978) (13467,-13467) (17956,-17956) (26934,-26934) (40401,-40401) (53868,-53868) (80802,-80802) (161604,-161604) (287296,13467) # # S = {2, 3, 71}: # (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) (71,-71) (71,54) (72,-71) (128,-3) (142,-142) (213,-213) (213,3) (284,-284) (426,-426) (639,-639) (852,-852) (1278,-1278) (2556,-2556) (5041,-5041) (5041,-128) (10082,-10082) (15123,-15123) (20164,-20164) (30246,-30246) (36352,-6561) (45369,-45369) (60492,-60492) (90738,-90738) (181476,-181476) (362952,-5041) # # S = {2, 3, 73}: # (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) (73,-73) (73,-72) (73,-9) (81,-73) (128,-3) (146,-146) (219,-219) (219,-192) (219,-3) (292,-292) (438,-438) (657,-657) (657,72) (876,-876) (1314,-1314) (2628,-2628) (4672,2187) (5329,-5329) (10658,-10658) (15552,73) (15987,-15987) (17496,-5329) (21316,-21316) (31974,-31974) (42632,243) (47961,-47961) (63948,-63948) (95922,-95922) (191844,-191844) (341056,47961) (383688,5329) (431649,-42632) # # S = {2, 3, 79}: # (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) (79,-79) (128,-3) (158,-158) (237,-237) (316,-316) (316,27) (324,-316) (474,-474) (711,-711) (711,18) (948,-948) (1422,-1422) (2133,64) (2844,-2844) (6241,-6241) (12482,-12482) (18723,-18723) (24964,-24964) (37446,-37446) (56169,-56169) (74892,-74892) (112338,-112338) (224676,-224676) (505521,-12482) # # S = {2, 3, 83}: # (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) (83,-83) (128,-3) (166,-166) (249,-249) (332,-332) (332,-324) (498,-498) (747,-747) (747,-18) (996,-996) (996,4) (1328,3) (1494,-1494) (2988,-2988) (6889,-6889) (13778,-13778) (20667,-20667) (27556,-27556) (41334,-41334) (62001,-62001) (82668,-82668) (124002,-124002) (248004,-248004) (558009,13778) # # S = {2, 3, 89}: # (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) (89,-89) (89,-81) (89,36) (128,-3) (178,-178) (267,-267) (356,-356) (432,-89) (534,-534) (801,-801) (801,-72) (1068,-1068) (1602,-1602) (3204,-3204) (7921,-7921) (15842,-15842) (23763,-23763) (31684,-31684) (47526,-47526) (71289,-71289) (95052,-95052) (142578,-142578) (285156,-285156) (641601,63368) # # S = {2, 3, 97}: # (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) (97,-97) (97,-96) (128,-3) (194,-194) (291,-291) (388,-388) (388,-324) (582,-582) (873,-873) (873,-144) (1164,-1164) (1746,-1746) (1746,-18) (3492,-3492) (9409,-9409) (18818,-18818) (28227,-28227) (37636,-37636) (56454,-56454) (84681,-84681) (112908,-112908) (169362,-169362) (338724,-338724) (762129,150544) (903264,9409)