# List of pairs of S-integers (x,y) satisfying # 0x^3 + 1x^2y + 1xy^2 + 0y^3 = m, where # m = 1, ..., 100 and # S is the set of the first 100 primes. # For each solution (x,y), only one of (x,y), (y,x) is listed. # It contains 492 pairs in total. # Format: "(x,y)". # Computing this list took 3473 seconds. # Authors: Rafael von Känel and Benjamin Matschke, 2015. # License: Creative commons 3.0 by-nc. # # m = 1: # # # m = 2: # (1,-2) (1,1) # # m = 3: # # # m = 4: # # # m = 5: # # # m = 6: # (3/20,-32/5) (289/777,-2646/629) (192027/319640,-429025/123464) (1,-3) (2,-3) (2,1) (476288/165715,-429025/123464) (476288/165715,192027/319640) (1369/357,-2646/629) (1369/357,289/777) (25/4,-32/5) (25/4,3/20) # # m = 7: # (289/2774,-5329/646) (234423/1588840,-1600225/229848) (1/2,-4) (16/15,-63/20) (25/12,-63/20) (25/12,16/15) (7/2,-4) (7/2,1/2) (1577536/231495,-1600225/229848) (1577536/231495,234423/1588840) (10108/1241,-5329/646) (10108/1241,289/2774) # # m = 8: # # # m = 9: # (1/2,-9/2) (441/340,-400/119) (289/140,-400/119) (289/140,441/340) (4,-9/2) (4,1/2) # # m = 10: # # # m = 11: # # # m = 12: # (361/3471,-18252/1691) (16/35,-75/14) (1,-4) (7254075/4091164,-8116801/2232980) (8248384/4430195,-8116801/2232980) (8248384/4430195,7254075/4091164) (3,-4) (3,1) (49/10,-75/14) (49/10,16/35) (7921/741,-18252/1691) (7921/741,361/3471) # # m = 13: # (4/21,-117/14) (1926544/2525565,-6315169/1394940) (13130325/3488044,-6315169/1394940) (13130325/3488044,1926544/2525565) (49/6,-117/14) (49/6,4/21) # # m = 14: # # # m = 15: # (16/143,-605/52) (3/2,-4) (5/2,-4) (5/2,3/2) (507/44,-605/52) (507/44,16/143) # # m = 16: # (2,-4) (2,2) # # m = 17: # (1/126,-324/7) (136025569/4284805140,-28341899537/1223915220) (11012403600/476211953,-28341899537/1223915220) (11012403600/476211953,136025569/4284805140) (833/18,-324/7) (833/18,1/126) # # m = 18: # # # m = 19: # (1/24,-171/8) (1050625/6303696,-16908544/1571325) (1089/3220,-23275/3036) (289/468,-1296/221) (9/10,-76/15) (729904/743745,-801025/162876) (4/3,-9/2) (18259/9810,-11881/2790) (8100/3379,-11881/2790) (8100/3379,18259/9810) (19/6,-9/2) (19/6,4/3) (690561/175420,-801025/162876) (690561/175420,729904/743745) (25/6,-76/15) (25/6,9/10) (3211/612,-1296/221) (3211/612,289/468) (8464/1155,-23275/3036) (8464/1155,1089/3220) (44651691/4214800,-16908544/1571325) (44651691/4214800,1050625/6303696) (64/3,-171/8) (64/3,1/24) # # m = 20: # (1/133,-980/19) (5/6,-16/3) (1,-5) (7744/6549,-12321/2596) (17405/4884,-12321/2596) (17405/4884,7744/6549) (4,-5) (4,1) (9/2,-16/3) (9/2,5/6) (361/7,-980/19) (361/7,1/133) # # m = 21: # # # m = 22: # (225/3268,-11552/645) (11/6,-9/2) (8/3,-9/2) (8/3,11/6) (20339/1140,-11552/645) (20339/1140,225/3268) # # m = 23: # # # m = 24: # # # m = 25: # # # m = 26: # (1/3,-9) (2809/2100,-20384/3975) (5625/1484,-20384/3975) (5625/1484,2809/2100) (26/3,-9) (26/3,1/3) # # m = 27: # # # m = 28: # (1/3,-28/3) (3025/2262,-7569/1430) (18928/4785,-7569/1430) (18928/4785,3025/2262) (9,-28/3) (9,1/3) # # m = 29: # # # m = 30: # (5/120019,-218089/257) (361/26877,-83521/1767) (10/117,-169/9) (5/56,-147/8) (1/6,-27/2) (28227/164131,-447458/33659) (375/1073,-1369/145) (27/55,-121/15) (1/2,-8) (25921/38868,-268960/38157) (1,-6) (12696/12533,-22801/3818) (11449/9291,-97470/17441) (96/77,-245/44) (34347/20470,-63368/12305) (578/341,-961/187) (179862147/90784540,-498436000/99567237) (2,-5) (961/476,-4335/868) (1568/527,-4335/868) (1568/527,961/476) (3,-5) (3,2) (165353881/54665580,-498436000/99567237) (165353881/54665580,179862147/90784540) (1815/527,-961/187) (1815/527,578/341) (66125/19046,-63368/12305) (66125/19046,34347/20470) (121/28,-245/44) (121/28,96/77) (26569/6099,-97470/17441) (26569/6099,11449/9291) (34445/6946,-22801/3818) (34445/6946,12696/12533) (5,-6) (5,1) (168507/26404,-268960/38157) (168507/26404,25921/38868) (15/2,-8) (15/2,1/2) (250/33,-121/15) (250/33,27/55) (1682/185,-1369/145) (1682/185,375/1073) (602045/45881,-447458/33659) (602045/45881,28227/164131) (40/3,-27/2) (40/3,1/6) (128/7,-147/8) (128/7,5/56) (243/13,-169/9) (243/13,10/117) (259470/5491,-83521/1767) (259470/5491,361/26877) (396294/467,-218089/257) (396294/467,5/120019) # # m = 31: # (4225/5754,-18769/2730) (54684/8905,-18769/2730) (54684/8905,4225/5754) # # m = 32: # # # m = 33: # (273529/1078446,-11177892/969119) (275/532,-784/95) (3/2,-11/2) (4,-11/2) (4,3/2) (1083/140,-784/95) (1083/140,275/532) (3433609/304386,-11177892/969119) (3433609/304386,273529/1078446) # # m = 34: # (1/2,-17/2) (121/60,-288/55) (425/132,-288/55) (425/132,121/60) (8,-17/2) (8,1/2) # # m = 35: # (12635/15996,-16641/2356) (4/3,-35/6) (9/2,-35/6) (9/2,4/3) (15376/2451,-16641/2356) (15376/2451,12635/15996) # # m = 36: # # # m = 37: # (1/30,-100/3) (1600/27573,-306397/12120) (7252/4209,-4761/854) (9/4,-16/3) (324/133,-1813/342) (361/126,-1813/342) (361/126,324/133) (37/12,-16/3) (37/12,9/4) (3721/966,-4761/854) (3721/966,7252/4209) (91809/3640,-306397/12120) (91809/3640,1600/27573) (333/10,-100/3) (333/10,1/30) # # m = 38: # # # m = 39: # # # m = 40: # # # m = 41: # # # m = 42: # (5041/57921,-201601/9159) (1,-7) (175/104,-384/65) (169/40,-384/65) (169/40,175/104) (6,-7) (6,1) (698922/31879,-201601/9159) (698922/31879,5041/57921) # # m = 43: # (1/14,-172/7) (52441/183540,-648025/52212) (2235312/184345,-648025/52212) (2235312/184345,52441/183540) (49/2,-172/7) (49/2,1/14) # # m = 44: # # # m = 45: # # # m = 46: # # # m = 47: # # # m = 48: # (3/10,-64/5) (578/777,-5292/629) (192027/159820,-429025/61732) (2,-6) (4,-6) (4,2) (952576/165715,-429025/61732) (952576/165715,192027/159820) (2738/357,-5292/629) (2738/357,578/777) (25/2,-64/5) (25/2,3/10) # # m = 49: # (4/33,-121/6) (441/22,-121/6) (441/22,4/33) # # m = 50: # (2/3,-9) (5408/2001,-21025/3588) (4761/1508,-21025/3588) (4761/1508,5408/2001) (25/3,-9) (25/3,2/3) # # m = 51: # (59643/56840,-153664/20445) (17/12,-27/4) (16/3,-27/4) (16/3,17/12) (357425/55272,-153664/20445) (357425/55272,59643/56840) # # m = 52: # # # m = 53: # (2495717/3405168,-3504384/394723) (3308761/406224,-3504384/394723) (3308761/406224,2495717/3405168) # # m = 54: # (3,-6) (3,3) # # m = 55: # # # m = 56: # (289/1387,-5329/323) (234423/794420,-1600225/114924) (1,-8) (32/15,-63/10) (25/6,-63/10) (25/6,32/15) (7,-8) (7,1) (3155072/231495,-1600225/114924) (3155072/231495,234423/794420) (20216/1241,-5329/323) (20216/1241,289/1387) # # m = 57: # # # m = 58: # (2/3,-29/3) (6272/2325,-8649/1400) (18125/5208,-8649/1400) (18125/5208,6272/2325) (9,-29/3) (9,2/3) # # m = 59: # # # m = 60: # # # m = 61: # (25/15624,-61504/315) (61/20,-25/4) (16/5,-25/4) (16/5,61/20) (242109/1240,-61504/315) (242109/1240,25/15624) # # m = 62: # (49/33,-558/77) (121/21,-558/77) (121/21,49/33) # # m = 63: # (1/4,-16) (16129/16120,-266175/31496) (61504/8255,-266175/31496) (61504/8255,16129/16120) (63/4,-16) (63/4,1/4) # # m = 64: # # # m = 65: # (1/88,-832/11) (13/84,-144/7) (1/4,-65/4) (26569/80494,-557780/39283) (3920/10653,-25281/1876) (5120/6413,-36517/3872) (2645/2822,-6889/782) (1849/1848,-7744/903) (52/45,-81/10) (38809/27778,-480740/63631) (13/6,-20/3) (2000719760/883654001,-1016270641/153785012) (5/2,-13/2) (21316/7449,-36481/5694) (98865/27886,-36481/5694) (98865/27886,21316/7449) (4,-13/2) (4,5/2) (768342961/176864692,-1016270641/153785012) (768342961/176864692,2000719760/883654001) (9/2,-20/3) (9/2,13/6) (104329/16942,-480740/63631) (104329/16942,38809/27778) (125/18,-81/10) (125/18,52/45) (28665/3784,-7744/903) (28665/3784,1849/1848) (15028/1909,-6889/782) (15028/1909,2645/2822) (14641/1696,-36517/3872) (14641/1696,5120/6413) (58357/4452,-25281/1876) (58357/4452,3920/10653) (755053/54442,-557780/39283) (755053/54442,26569/80494) (16,-65/4) (16,1/4) (245/12,-144/7) (245/12,13/84) (605/8,-832/11) (605/8,1/88) # # m = 66: # # # m = 67: # (1459264/7082019,-117272043/6466424) (28654609/1598184,-117272043/6466424) (28654609/1598184,1459264/7082019) # # m = 68: # (17/15,-25/3) (207025/99258,-725904/106015) (922913/193830,-725904/106015) (922913/193830,207025/99258) (36/5,-25/3) (36/5,17/15) # # m = 69: # (1/2,-12) (2209/1100,-14375/2068) (5808/1175,-14375/2068) (5808/1175,2209/1100) (23/2,-12) (23/2,1/2) # # m = 70: # (289/689,-11830/901) (7/12,-45/4) (2,-7) (484183/206184,-645248/95469) (658845/149384,-645248/95469) (658845/149384,484183/206184) (5,-7) (5,2) (32/3,-45/4) (32/3,7/12) (2809/221,-11830/901) (2809/221,289/689) # # m = 71: # (15876/8471,-38809/5418) (131279/24822,-38809/5418) (131279/24822,15876/8471) # # m = 72: # (1,-9) (441/170,-800/119) (289/70,-800/119) (289/70,441/170) (8,-9) (8,1) # # m = 73: # # # m = 74: # # # m = 75: # (1/2,-25/2) (2401/1196,-8112/1127) (13225/2548,-8112/1127) (13225/2548,2401/1196) (12,-25/2) (12,1/2) # # m = 76: # # # m = 77: # # # m = 78: # (800/551,-4693/580) (3/2,-8) (13/2,-8) (13/2,3/2) (2523/380,-4693/580) (2523/380,800/551) # # m = 79: # (16/39,-169/12) (711/52,-169/12) (711/52,16/39) # # m = 80: # # # m = 81: # # # m = 82: # # # m = 83: # # # m = 84: # (7/110,-400/11) (104329/48063,-1034964/139859) (3,-7) (4,-7) (4,3) (187489/35853,-1034964/139859) (187489/35853,104329/48063) (363/10,-400/11) (363/10,7/110) # # m = 85: # (1/6,-68/3) (73441/110148,-844605/72628) (1221008/111381,-844605/72628) (1221008/111381,73441/110148) (45/2,-68/3) (45/2,1/6) # # m = 86: # (5203/24780,-31329/1540) (25/39,-774/65) (43/63,-81/7) (2738/1725,-22747/2775) (79507/48111,-82418/10191) (8/3,-43/6) (9/2,-43/6) (9/2,8/3) (56169/8729,-82418/10191) (56169/8729,79507/48111) (5625/851,-22747/2775) (5625/851,2738/1725) (98/9,-81/7) (98/9,43/63) (169/15,-774/65) (169/15,25/39) (39200/1947,-31329/1540) (39200/1947,5203/24780) # # m = 87: # (29/70,-147/10) (100/7,-147/10) (100/7,29/70) # # m = 88: # # # m = 89: # (1296/689,-15041/1908) (2809/468,-15041/1908) (2809/468,1296/689) # # m = 90: # (185761/338793,-1540081/117663) (1,-10) (640/209,-1089/152) (361/88,-1089/152) (361/88,640/209) (9,-10) (9,1) (6707610/534871,-1540081/117663) (6707610/534871,185761/338793) # # m = 91: # (1/18,-81/2) (41616/523435,-2356225/69564) (529/1974,-40131/2162) (124579/219480,-222784/17205) (891517900/929817009,-960814009/93890610) (24964/15675,-75625/9006) (9/4,-91/12) (91/30,-36/5) (25/6,-36/5) (25/6,91/30) (16/3,-91/12) (16/3,9/4) (295659/43450,-75625/9006) (295659/43450,24964/15675) (899820009/97020610,-960814009/93890610) (899820009/97020610,891517900/929817009) (216225/17464,-222784/17205) (216225/17464,124579/219480) (8836/483,-40131/2162) (8836/483,529/1974) (10581571/313140,-2356225/69564) (10581571/313140,41616/523435) (364/9,-81/2) (364/9,1/18) # # m = 92: # (4/3,-9) (3249/1550,-22103/2850) (10000/1767,-22103/2850) (10000/1767,3249/1550) (23/3,-9) (23/3,4/3) # # m = 93: # # # m = 94: # (47/3150,-3969/50) (5000/63,-3969/50) (5000/63,47/3150) # # m = 95: # # # m = 96: # (722/3471,-36504/1691) (32/35,-75/7) (2,-8) (7254075/2045582,-8116801/1116490) (16496768/4430195,-8116801/1116490) (16496768/4430195,7254075/2045582) (6,-8) (6,2) (49/5,-75/7) (49/5,32/35) (15842/741,-36504/1691) (15842/741,722/3471) # # m = 97: # (25/42,-196/15) (719044225/300522012,-7185803553/936272540) (1219127056/230796705,-7185803553/936272540) (1219127056/230796705,719044225/300522012) (873/70,-196/15) (873/70,25/42) # # m = 98: # (126025/101688,-2264192/237495) (9/5,-25/3) (98/15,-25/3) (98/15,9/5) (447561/53960,-2264192/237495) (447561/53960,126025/101688) # # m = 99: # # # m = 100: #