# 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, 5, p}, # where p ranges over all other primes less or equal to 31. # It contains 1217 pairs (x,y), some of which may appear for more than one S. # Format: "(x,y)". # Computing this list took 8724 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) (3,-3) (3,-2) (4,-4) (4,-3) (4,4) (5,-5) (5,-4) (5,3) (6,-6) (6,-5) (6,2) (7,-7) (7,-6) (7,1) (8,-7) (9,-9) (9,-8) (9,-1) (10,-10) (10,-9) (10,-2) (12,-12) (12,-4) (14,-14) (14,-6) (15,-15) (15,-14) (15,-7) (15,12) (16,-15) (18,-18) (18,-10) (18,9) (20,-20) (20,-12) (20,7) (21,-21) (21,-20) (21,6) (24,3) (25,-25) (25,-24) (25,2) (28,-28) (28,-27) (28,-20) (28,-1) (30,-30) (30,-3) (32,-5) (35,-35) (35,-27) (35,-8) (36,-36) (36,-35) (36,-28) (36,-9) (36,28) (42,-42) (42,-15) (45,-45) (45,-18) (48,-21) (49,-49) (49,-48) (49,15) (50,-50) (50,-49) (50,-42) (50,14) (54,10) (60,-60) (60,4) (63,-63) (63,-36) (63,1) (64,-63) (70,-70) (70,-6) (72,-45) (75,-75) (75,-48) (75,50) (80,45) (81,-80) (84,-84) (84,-20) (90,-90) (90,-63) (90,35) (98,-98) (98,-90) (98,27) (100,-100) (100,-36) (100,25) (105,-105) (105,20) (108,-100) (120,5) (125,-98) (126,-126) (126,-125) (126,-1) (126,90) (128,-3) (135,-10) (140,-140) (140,-15) (147,-147) (147,-120) (150,-150) (150,-25) (160,-35) (162,-98) (175,-175) (175,-50) (175,168) (180,-180) (180,36) (189,-125) (189,-64) (196,-196) (196,20) (196,147) (200,-75) (210,-210) (210,6) (225,-225) (225,-224) (225,-100) (225,-9) (243,100) (245,-245) (245,-120) (245,98) (252,-252) (252,-225) (252,-36) (280,63) (294,-294) (294,49) (300,-300) (300,-175) (300,-84) (315,-315) (315,-288) (315,28) (336,7) (350,-350) (350,-225) (350,-7) (350,162) (375,-32) (378,-35) (392,-49) (405,-280) (420,-420) (441,-441) (441,-225) (441,-98) (441,288) (448,-105) (450,-450) (490,-490) (490,-147) (500,12) (504,225) (525,-525) (525,-400) (540,-28) (567,-224) (588,-588) (588,-245) (630,-630) (700,-700) (700,300) (720,9) (735,-735) (735,-392) (735,-6) (750,-686) (750,-21) (784,-441) (800,-675) (882,-882) (900,-900) (900,100) (972,28) (980,-980) (980,-972) (980,20) (1029,-300) (1050,-1050) (1050,-50) (1152,-1125) (1225,-1225) (1225,-882) (1225,-225) (1225,972) (1250,81) (1260,-1260) (1296,35) (1323,-980) (1323,8) (1350,-1225) (1350,-350) (1470,-1470) (1568,-1225) (1575,-1575) (1715,-384) (1764,-1764) (1764,-36) (1764,980) (1792,405) (1800,1575) (1875,-147) (2100,-2100) (2187,10) (2205,-2205) (2205,-8) (2304,-1575) (2401,-2400) (2450,-2450) (2450,294) (2646,98) (2940,-2940) (2940,-196) (3072,-875) (3087,288) (3150,-3150) (3150,225) (3200,175) (3360,15) (3430,-2430) (3500,-756) (3600,-225) (3675,-3675) (3675,-300) (3969,-1225) (4116,-20) (4375,-4374) (4375,-4032) (4410,-4410) (4900,-4900) (6075,784) (6125,3136) (6300,-6300) (6615,-6272) (6860,-1) (7056,2205) (7350,-7350) (8000,-3087) (8100,-100) (8820,-8820) (8820,441) (9216,45) (9408,-147) (10935,-9604) (11025,-11025) (11025,-1764) (12005,162) (12250,-11907) (14400,-11025) (14400,1225) (14700,-14700) (22050,-22050) (22050,-98) (25725,-25600) (33075,9800) (36000,-63) (39200,3675) (42525,350) (44100,-44100) (44100,-1225) (50625,28) (62720,-19845) (73500,588) (117600,49) (157500,-36) (216090,-90) (274400,225) (328125,384) (401408,55125) (5358150,1225) # # S = {2, 3, 5, 11}: # (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) (11,-11) (11,-10) (11,-3) (12,-12) (12,-11) (12,-4) (15,-15) (15,12) (16,-15) (16,11) (18,-18) (18,-10) (18,9) (20,-20) (20,-12) (22,-22) (22,5) (24,3) (25,-25) (25,-24) (25,2) (30,-30) (30,-22) (30,-3) (32,-5) (33,-33) (33,-32) (33,-25) (33,-6) (36,-36) (36,-9) (44,-44) (44,-36) (44,20) (45,-45) (45,-44) (45,-18) (50,-50) (54,10) (55,-55) (55,-54) (55,9) (60,-60) (60,-33) (60,4) (66,-66) (66,-2) (72,-45) (75,-75) (75,-48) (75,-11) (75,50) (80,45) (81,-80) (81,44) (90,-90) (99,-99) (99,-72) (100,-100) (100,-99) (100,-36) (100,25) (108,-100) (108,-44) (110,-110) (110,15) (120,5) (121,-121) (121,-120) (121,4) (128,-3) (132,-132) (135,-10) (150,-150) (150,-25) (150,66) (165,-165) (165,-40) (180,-180) (180,-55) (180,36) (192,-165) (198,-198) (198,18) (200,-75) (220,-220) (220,-4) (225,-225) (225,-198) (225,-100) (225,-9) (242,-242) (243,-242) (243,100) (250,-242) (270,242) (275,-275) (275,-150) (288,55) (300,-300) (330,-330) (352,-9) (363,-363) (363,-20) (375,-32) (396,-396) (396,-180) (400,-275) (450,-450) (484,-484) (495,-495) (500,12) (550,-550) (550,-486) (550,450) (605,-605) (605,-480) (640,-297) (660,-660) (675,-550) (704,25) (720,9) (726,-726) (726,3) (726,605) (800,-675) (825,-825) (825,-96) (891,440) (900,-900) (900,100) (968,-625) (968,363) (990,-990) (990,10) (1056,275) (1089,-1089) (1089,-360) (1089,242) (1100,-1100) (1100,-100) (1125,-396) (1152,-1125) (1210,-1210) (1210,121) (1250,81) (1320,11) (1375,-44) (1452,-1452) (1452,-121) (1650,-1650) (1815,-1815) (1815,-484) (1936,-605) (1980,-1980) (2178,-2178) (2178,-450) (2187,10) (2200,-3) (2420,-2420) (2420,-1089) (2420,324) (2475,-2475) (2475,900) (2560,-363) (2700,44) (2750,-6) (2816,-1485) (2880,495) (3025,-3025) (3025,-2025) (3267,-1936) (3300,-3300) (3300,75) (3600,-225) (3630,-3630) (3645,-3520) (4356,-4356) (4356,-3025) (4950,-4950) (5346,-1250) (5445,-5445) (6050,-6050) (6400,-3025) (6875,-16) (7260,-7260) (8100,-100) (9075,-9075) (9075,-7744) (9216,45) (9900,-9900) (10692,-44) (10890,-10890) (10890,-242) (11979,-11250) (11979,-5120) (12100,-12100) (12100,-1452) (12288,-121) (13068,-2420) (18150,-18150) (21780,-21780) (27225,-27225) (27225,-225) (27225,8712) (28125,22528) (30250,-19602) (33275,9600) (34848,1089) (36300,-36300) (36300,-363) (39204,100) (54450,-54450) (59895,-576) (66825,-51200) (88209,-3025) (108900,-108900) (133100,-8100) (147015,19360) (163350,3025) (193600,-27225) (378125,78408) (441045,15488) (614400,-275) (743424,226875) # # S = {2, 3, 5, 13}: # (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) (13,-13) (13,-12) (13,-5) (15,-15) (15,12) (16,-15) (18,-18) (18,-10) (18,9) (20,-20) (20,-12) (24,3) (25,-25) (25,-24) (25,2) (26,-26) (26,-25) (26,-18) (26,1) (27,-26) (30,-30) (30,-3) (32,-5) (36,-36) (36,-9) (39,-39) (39,-12) (39,25) (40,-39) (40,-13) (45,-45) (45,-18) (50,-50) (52,-52) (52,-25) (52,12) (54,10) (60,-60) (60,-52) (60,4) (65,-65) (65,-64) (65,-1) (65,60) (72,-45) (75,-75) (75,-48) (75,50) (78,-78) (80,45) (81,-80) (90,-90) (90,-26) (100,-100) (100,-36) (100,25) (108,-100) (117,-117) (117,-90) (117,8) (120,5) (125,-117) (128,-3) (130,-130) (130,-5) (135,-10) (144,-117) (150,-150) (150,-25) (156,-156) (156,60) (169,-169) (180,-180) (180,36) (195,-195) (200,-75) (208,135) (225,-225) (225,-100) (225,-9) (234,-234) (234,-18) (243,100) (260,-260) (260,-135) (300,-300) (320,-195) (324,-260) (325,-325) (325,-324) (325,-200) (325,18) (338,-338) (338,5) (351,-8) (375,-32) (390,-390) (450,-450) (450,-325) (450,-234) (468,-468) (468,-125) (486,26) (500,12) (507,-507) (507,-480) (507,5) (512,-169) (585,-585) (585,144) (625,-624) (625,104) (650,-650) (675,325) (676,-676) (676,-675) (676,324) (720,9) (768,-39) (780,-780) (800,-675) (845,-845) (845,-720) (845,486) (900,-900) (900,100) (975,-975) (975,25) (1014,-1014) (1152,-1125) (1170,-1170) (1250,81) (1300,-1300) (1300,-300) (1352,845) (1500,-169) (1521,-1521) (1521,676) (1690,-1690) (1690,507) (1872,325) (1950,-1950) (2028,-2028) (2028,-300) (2028,169) (2080,117) (2187,10) (2250,-1521) (2340,-2340) (2400,975) (2535,-2535) (2535,-338) (2704,-507) (2925,-2925) (2925,450) (3042,-3042) (3042,-845) (3250,-1053) (3380,-3380) (3380,-5) (3600,-225) (3900,-3900) (4225,-4225) (4225,-2028) (5070,-5070) (5850,-5850) (5850,-18) (6084,-6084) (6760,-4563) (7605,-7605) (7605,-5408) (8100,-100) (8450,-8450) (8450,-450) (9126,8450) (9216,45) (9984,-3125) (10140,-10140) (11700,-11700) (12168,-1) (12675,-12675) (12800,-12675) (15210,-15210) (15600,25) (16900,-16900) (16900,676) (17550,26) (18225,-13312) (18225,-2600) (18252,-676) (19773,-90) (21970,-18) (25350,-25350) (30420,-30420) (38025,-38025) (43200,-325) (43264,-41067) (50700,-50700) (57122,-2250) (59904,-585) (60840,-1521) (63375,-4056) (76050,-76050) (97344,-38025) (98415,5408) (123201,-105625) (152100,-152100) (163840,2535) (164775,1600) (166400,-25) (219700,-218700) (270400,4225) (273780,845) (342225,-67600) (3802500,-6084) # # S = {2, 3, 5, 17}: # (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) (17,-17) (17,-16) (17,-9) (17,10) (18,-18) (18,-17) (18,-10) (18,9) (20,-20) (20,-12) (24,3) (25,-25) (25,-24) (25,-17) (25,2) (30,-30) (30,-3) (32,-5) (34,-34) (34,30) (36,-36) (36,-9) (45,-45) (45,-18) (50,-50) (51,-51) (51,-50) (51,-24) (54,10) (60,-60) (60,4) (68,-68) (68,-60) (68,-4) (72,-45) (75,-75) (75,-48) (75,50) (80,45) (81,-80) (81,-17) (85,-85) (85,40) (90,-90) (100,-100) (100,-36) (100,25) (102,-102) (102,-75) (108,-100) (108,17) (120,5) (128,-3) (135,-10) (136,-135) (150,-150) (150,-25) (153,-153) (170,-170) (170,-162) (170,-45) (180,-180) (180,-153) (180,36) (200,-75) (204,-204) (204,12) (225,-225) (225,-100) (225,-9) (243,100) (250,-34) (255,-255) (256,-255) (289,-289) (289,-288) (289,-225) (289,54) (300,-300) (306,-306) (306,-90) (340,-340) (340,3) (360,-17) (375,-32) (425,-425) (425,-300) (450,-450) (500,12) (510,-510) (510,2) (576,153) (578,-578) (612,-612) (612,-100) (720,9) (765,-765) (765,-640) (765,-36) (768,-425) (800,-675) (850,-850) (850,150) (867,-867) (900,-900) (900,100) (1020,-1020) (1020,-20) (1088,243) (1152,-1125) (1156,-1156) (1250,81) (1275,-1275) (1280,51) (1445,-1445) (1530,-1530) (1620,-289) (1700,-1700) (1734,-1734) (1734,-6) (1875,-544) (2125,72) (2187,10) (2312,-2187) (2550,-2550) (2601,-2601) (2601,2312) (2700,-1700) (2754,-10) (2890,-2890) (3060,-3060) (3400,-25) (3456,-2125) (3468,-3468) (3468,-3125) (3468,1445) (3600,-225) (3825,-3825) (3825,-450) (3825,1088) (4335,-4335) (4335,-960) (4335,578) (4624,289) (4896,17) (5100,-5100) (5202,-5202) (5202,-289) (5625,-4896) (5780,-5780) (5780,-867) (6400,459) (7200,-3825) (7225,-7225) (7225,-2312) (7650,-7650) (7803,-2890) (8100,-100) (8670,-8670) (9216,45) (9248,-4335) (10000,-7803) (10404,-10404) (12150,17) (13005,-13005) (13600,2025) (14450,-14450) (15300,-15300) (17340,-17340) (20808,-1125) (21675,-21675) (23409,-18496) (24000,-14739) (26010,-26010) (28900,-28900) (28900,10404) (36125,-31212) (37179,2125) (39015,289) (43350,-43350) (52020,-52020) (65025,-65025) (86700,-86700) (104448,-625) (110976,21675) (130050,-130050) (130050,2601) (140625,-17) (260100,-260100) (361250,-46818) (417605,-393216) (585225,28900) (1419857,23040) (1685448,-289) (16646400,-65025) (25095825,3276800) # # S = {2, 3, 5, 19}: # (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) (19,-19) (19,-18) (19,8) (20,-20) (20,-19) (20,-12) (24,3) (25,-25) (25,-24) (25,2) (27,-19) (30,-30) (30,-3) (32,-5) (36,-36) (36,-9) (38,-38) (38,-30) (45,-45) (45,-18) (45,19) (50,-50) (54,10) (57,-57) (57,-30) (60,-60) (60,4) (72,-45) (75,-75) (75,-48) (75,50) (76,-76) (76,-75) (76,-12) (80,45) (81,-80) (90,-90) (95,-95) (95,30) (96,-95) (100,-100) (100,-36) (100,25) (108,-100) (114,-114) (114,-50) (120,5) (128,-3) (135,-10) (144,-19) (150,-150) (150,-25) (152,-125) (152,-27) (171,-171) (171,-144) (171,45) (180,-180) (180,36) (190,-190) (200,-75) (225,-225) (225,-100) (225,-9) (228,-228) (228,-12) (243,100) (285,-285) (285,-160) (300,-300) (324,19) (342,-342) (342,1) (361,-361) (361,-360) (361,-18) (375,-32) (380,-380) (400,-57) (450,-450) (475,-475) (486,-361) (500,12) (513,-512) (513,-1) (570,-570) (600,-475) (684,-684) (684,45) (720,9) (722,-722) (800,-675) (810,190) (855,-855) (855,-512) (900,-900) (900,-684) (900,-171) (900,100) (950,-950) (950,50) (1083,-1083) (1140,-1140) (1152,-1125) (1216,-1215) (1250,81) (1350,-19) (1425,-1425) (1444,-1444) (1500,228) (1710,-1710) (1710,18) (1805,-1805) (1900,-1900) (1900,-900) (2025,-1900) (2166,-2166) (2187,10) (2850,-2850) (2888,2025) (3249,-3249) (3420,-3420) (3420,-45) (3600,-225) (3610,-3610) (3610,486) (3610,3249) (4275,-4275) (4275,-900) (4332,-4332) (4332,1500) (4800,-1425) (5415,-5415) (5415,1444) (5700,-5700) (5776,1083) (6144,-5415) (6498,-6498) (6498,361) (6840,19) (7220,-7220) (7220,-361) (8100,-100) (8550,-8550) (8664,-1805) (8748,1900) (9025,-9025) (9025,-2166) (9216,45) (9234,-2375) (9375,-114) (9747,-2888) (10830,-10830) (12996,-12996) (16245,-16245) (17100,-17100) (18050,-18050) (20577,15360) (21660,-21660) (23104,-16245) (27075,-27075) (27075,-75) (32490,-32490) (36100,-36100) (36100,-29241) (45125,-20736) (45125,9747) (51984,-45125) (54150,-54150) (54150,722) (58482,-3610) (64980,-64980) (81225,-81225) (91200,-75) (103968,81225) (108300,-108300) (162450,-162450) (184832,361) (296875,3888) (324900,-324900) (342950,50) (438615,361) (866400,-9025) (972800,-115425) # # S = {2, 3, 5, 23}: # (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) (23,-23) (23,-15) (23,4) (24,-23) (24,3) (25,-25) (25,-24) (25,2) (30,-30) (30,-3) (32,-5) (36,-36) (36,-9) (45,-45) (45,-18) (46,-46) (46,-45) (46,18) (50,-50) (50,-23) (54,-46) (54,10) (60,-60) (60,4) (69,-69) (69,-5) (72,-45) (75,-75) (75,-48) (75,50) (80,45) (81,-80) (90,-90) (92,-92) (96,-69) (100,-100) (100,-92) (100,-36) (100,25) (108,-100) (115,-115) (115,10) (120,5) (128,-3) (135,-10) (138,-138) (150,-150) (150,-25) (180,-180) (180,36) (200,-75) (207,-207) (207,-180) (207,9) (225,-225) (225,-100) (225,-9) (230,-230) (240,-115) (243,100) (276,-276) (276,-60) (300,-300) (320,23) (345,-345) (345,-2) (368,-243) (368,-25) (375,-32) (384,345) (414,-414) (450,-450) (460,-460) (500,12) (529,-529) (529,200) (540,460) (575,-575) (575,-450) (576,-575) (690,-690) (720,9) (800,-675) (828,-828) (900,-900) (900,100) (900,828) (972,-460) (1035,-1035) (1058,-1058) (1104,-375) (1150,-1150) (1150,-150) (1152,-1125) (1250,-1242) (1250,81) (1380,-1380) (1587,-1587) (1587,-256) (1725,-1725) (1725,-1600) (1725,3) (2070,-2070) (2116,-2116) (2116,81) (2187,10) (2300,-2300) (2645,-2645) (3174,-3174) (3450,-3450) (3450,-75) (3600,-225) (3645,-2645) (4050,46) (4140,-4140) (4761,-4761) (4761,4500) (4860,-2116) (5120,-207) (5175,-5175) (5175,-1800) (5290,-5290) (5625,207) (6348,-6348) (6900,-6900) (7935,-7935) (7935,4232) (8100,-100) (9216,45) (9522,-9522) (9522,2645) (10350,-10350) (10580,-10580) (10580,1587) (11250,-9522) (12696,-529) (13225,-13225) (13225,-1058) (13225,2400) (14283,-2116) (14375,-2208) (15525,100) (15870,-15870) (16200,-575) (16767,-4600) (16928,-4761) (19044,-19044) (20700,-20700) (23805,-23805) (25392,-13225) (26450,-26450) (26450,-14283) (31740,-31740) (36800,6075) (39675,-39675) (39675,3200) (47610,-47610) (52900,-52900) (79350,-79350) (83835,-40960) (92160,-1035) (95220,-95220) (95220,2116) (119025,-119025) (158700,-158700) (238050,-238050) (287500,-4) (304704,23805) (330625,-2116) (342792,-330625) (476100,-476100) (514188,264500) (1083392,-1071225) (1523520,-2645) (3213675,-1692800) # # S = {2, 3, 5, 29}: # (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) (29,-29) (29,-2) (30,-30) (30,-29) (30,-3) (32,-5) (36,-36) (36,-9) (45,-45) (45,-18) (50,-50) (54,10) (58,-58) (58,-50) (58,6) (60,-60) (60,4) (72,-45) (75,-75) (75,-48) (75,50) (80,45) (81,-80) (87,-87) (87,-60) (90,-90) (96,29) (100,-100) (100,-36) (100,25) (108,-100) (116,-116) (116,-108) (116,9) (116,100) (120,5) (128,-3) (135,-10) (145,-145) (145,-144) (145,-81) (145,-20) (150,-150) (150,-25) (174,-174) (180,-180) (180,-116) (180,36) (200,-75) (225,-225) (225,-100) (225,-9) (243,100) (256,87) (261,-261) (261,-45) (270,-145) (288,-261) (290,-290) (300,-300) (348,-348) (348,-5) (375,-348) (375,-32) (435,-435) (450,-450) (500,12) (522,-522) (522,-10) (580,-580) (720,9) (725,-725) (725,-600) (725,4) (800,-675) (841,-841) (841,-625) (870,-870) (900,-900) (900,100) (1044,-1044) (1152,-1125) (1215,116) (1250,81) (1305,-1305) (1305,-576) (1450,-1450) (1450,-450) (1458,-1450) (1682,-1682) (1740,-1740) (1740,-12) (2025,-1682) (2175,-2175) (2175,1200) (2187,10) (2250,-522) (2523,-2523) (2610,-2610) (2900,-2900) (3125,-928) (3364,-3364) (3600,-225) (4205,-4205) (4350,-4350) (5000,-87) (5046,-5046) (5220,-5220) (6525,-6525) (6525,-6400) (7047,5120) (7569,-7569) (8100,-100) (8410,-8410) (8700,-8700) (9000,261) (9216,45) (10092,-10092) (11136,-1875) (12615,-12615) (13050,-13050) (15138,-15138) (16820,-16820) (16820,7569) (18125,6264) (20184,4205) (21025,-21025) (21025,-5400) (21025,3364) (22707,1682) (25230,-25230) (25230,-841) (26100,-26100) (26100,900) (26912,-2523) (30276,-30276) (37845,-37845) (37845,-13456) (42050,-42050) (45414,-21025) (48778,1875) (50460,-50460) (59392,-59049) (63075,-63075) (68121,800) (75690,-75690) (84100,-84100) (105125,-80736) (126150,-126150) (151380,-151380) (189225,-189225) (210250,-15138) (252300,-252300) (378450,-378450) (645888,12615) (756900,-756900) (1703025,1345600) (3027600,21025) (3065445,-16820) # # S = {2, 3, 5, 31}: # (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) (31,-31) (31,-30) (31,-4) (32,-31) (32,-5) (36,-36) (36,-9) (45,-45) (45,-18) (50,-50) (54,10) (60,-60) (60,4) (62,-62) (62,-54) (62,2) (72,-45) (75,-75) (75,-48) (75,50) (80,45) (81,-80) (90,-90) (93,-93) (93,32) (100,-100) (100,-36) (100,25) (108,-100) (120,-93) (120,5) (124,-124) (124,-60) (124,1) (125,-124) (128,-3) (135,-10) (150,-150) (150,-25) (155,-155) (155,-128) (155,-30) (180,-180) (180,36) (186,-186) (186,30) (200,-75) (225,-225) (225,-100) (225,-9) (243,100) (250,-186) (250,93) (279,-279) (279,64) (300,-300) (310,-310) (372,-372) (375,-32) (405,-62) (450,-450) (450,62) (450,279) (465,-465) (500,12) (558,-558) (620,-620) (620,-108) (720,9) (744,-15) (775,-775) (775,-432) (775,225) (800,-675) (900,-900) (900,-775) (900,100) (930,-930) (961,-961) (961,-960) (1116,-1116) (1116,-900) (1152,-1125) (1250,81) (1395,-1395) (1395,-64) (1550,-1550) (1620,-620) (1860,-1860) (1922,-1922) (2187,10) (2325,-2325) (2325,-128) (2790,-2790) (2883,-2883) (3100,-3100) (3600,-225) (3840,-465) (3844,-3844) (4650,-4650) (4805,-4805) (4805,108) (5580,-5580) (5766,-5766) (6200,-6075) (6975,-6975) (6975,-3600) (8100,-100) (8649,-8649) (9216,45) (9300,-9300) (9610,-9610) (11532,-11532) (11664,-4805) (13950,-13950) (14415,-14415) (15376,14415) (17298,-17298) (19220,-19220) (24025,-24025) (24025,5766) (25947,3844) (27900,-27900) (27900,-900) (28830,-28830) (28830,961) (29760,31) (30752,-961) (34596,-34596) (34596,-4805) (35712,225) (38440,-8649) (39366,-62) (43245,-43245) (48050,-48050) (57660,-57660) (72075,-72075) (77841,-48050) (78732,775) (86490,-86490) (96100,-96100) (144150,-144150) (172980,-172980) (216225,-216225) (216225,-225) (233523,4805) (240250,-1922) (246016,-216225) (288300,-288300) (432450,-432450) (864900,-864900) (1081125,-276768) (3075200,648675) (75078125,-35426304)