# List of pairs of S-integers (x,y) satisfying # 1x^3 + 2x^2y + 3xy^2 + 4y^3 = m, where # m = 1, ..., 100 and # S is the set of the first 100 primes. # It contains 132 pairs in total. # Format: "(x,y)". # Computing this list took 11236 seconds. # Authors: Rafael von Känel and Benjamin Matschke, 2015. # License: Creative commons 3.0 by-nc. # # m = 1: # (1,0) (10/7,-9/14) # # m = 2: # (-13309/151,8063/151) (-65315/12428,159569/49712) (-314/131,411/262) (-1,1) (-155/371,327/371) (-2/29,47/58) (1/2,5/8) (94/59,-33/59) (2,-1) (5,-3) # # m = 3: # # # m = 4: # (-2,3/2) (0,1) (637/421,177/1684) # # m = 5: # (-3,2) (103/59,-13/236) (2,-1/2) # # m = 6: # # # m = 7: # # # m = 8: # (2,0) (20/7,-9/7) # # m = 9: # # # m = 10: # (-14,17/2) (1,1) # # m = 11: # # # m = 12: # # # m = 13: # (-647/259,2125/1036) (6,-7/2) # # m = 14: # (2,1/2) (3,-1) (3251/529,-7585/2116) # # m = 15: # # # m = 16: # (-26618/151,16126/151) (-65315/6214,159569/24856) (-628/131,411/131) (-2,2) (-310/371,654/371) (-4/29,47/29) (1,5/4) (188/59,-66/59) (4,-2) (10,-6) # # m = 17: # # # m = 18: # # # m = 19: # # # m = 20: # # # m = 21: # # # m = 22: # # # m = 23: # (-33,20) (-226/169,697/338) (-1,2) (3,-1/4) (2857/794,-4019/3176) # # m = 24: # # # m = 25: # # # m = 26: # (2,1) (1006/47,-1217/94) # # m = 27: # (3,0) (30/7,-27/14) # # m = 28: # (-8,5) (10250/2279,-9631/4558) # # m = 29: # # # m = 30: # # # m = 31: # (-3494/1357,6823/2714) (7,-4) # # m = 32: # (-4,3) (0,2) (1274/421,177/842) # # m = 33: # # # m = 34: # # # m = 35: # (23/13,18/13) # # m = 36: # # # m = 37: # (-2,5/2) # # m = 38: # # # m = 39: # # # m = 40: # (-6,4) (206/59,-13/118) (4,-1) # # m = 41: # # # m = 42: # # # m = 43: # # # m = 44: # # # m = 45: # # # m = 46: # # # m = 47: # (-17939/173,43473/692) (-17/2,43/8) (-10/37,173/74) (2,3/2) (113/7,-68/7) (547/29,-330/29) # # m = 48: # # # m = 49: # (-2098/227,2633/454) (1,2) # # m = 50: # # # m = 51: # # # m = 52: # # # m = 53: # (-8015/7136,74357/28544) (994/461,1399/922) (5,-2) # # m = 54: # (-39927/151,24189/151) (-195945/12428,478707/49712) (-942/131,1233/262) (-3,3) (-465/371,981/371) (-6/29,141/58) (3/2,15/8) (282/59,-99/59) (6,-3) (15,-9) # # m = 55: # # # m = 56: # # # m = 57: # # # m = 58: # (-62/13,47/13) (-975/281,893/281) (3,1) (1790/191,-1037/191) (13,-31/4) # # m = 59: # (-13,8) (-13363/2623,9850/2623) (39/14,67/56) (54/13,-11/26) # # m = 60: # # # m = 61: # # # m = 62: # (5,-7/4) # # m = 63: # # # m = 64: # (4,0) (40/7,-18/7) # # m = 65: # (-1,11/4) (149/61,94/61) # # m = 66: # # # m = 67: # # # m = 68: # # # m = 69: # # # m = 70: # (-137,83) (-2,3) (-86/103,573/206) (188263/44161,-9797/44161) (473/101,-97/101) (37414306/546157,-45327503/1092314) # # m = 71: # # # m = 72: # # # m = 73: # # # m = 74: # # # m = 75: # # # m = 76: # # # m = 77: # # # m = 78: # # # m = 79: # # # m = 80: # (-28,17) (2,2) # # m = 81: # # # m = 82: # # # m = 83: # # # m = 84: # # # m = 85: # # # m = 86: # (-18,11) (-331/43,221/43) (-158/23,109/23) (-1875/499,1781/499) (-102/31,107/31) (-502/157,1077/314) (-1,3) (-1311/2773,32069/11092) (6270/4901,11689/4901) (173/97,211/97) (505/233,1853/932) (83285/21883,16837/21883) (27/7,5/7) (383/79,-229/316) (5,-1) (590379/117349,-123925/117349) (6,-5/2) (48925/5222,-110703/20888) (82757/7897,-47805/7897) (1947/181,-1129/181) (69/2,-167/8) (38,-23) (20561/271,-12455/271) # # m = 87: # # # m = 88: # # # m = 89: # # # m = 90: # # # m = 91: # (-5,4) # # m = 92: # # # m = 93: # # # m = 94: # (-35/13,177/52) (29/23,57/23) (1242/227,-361/227) (9,-5) # # m = 95: # # # m = 96: # # # m = 97: # (-23,14) (241/46,-203/184) # # m = 98: # (-13/7,23/7) # # m = 99: # # # m = 100: #