# Sum of powers a4 + b2 = c3

1. Alpertron
2. Number Theory
3. Sum of powers a4 + b2 = c3

The following is a list of sum of powers: a4 + b2 = c3 where gcd(a,b,c) = 1. If you have any comment please fill the form.

1. 34 + 462 = 133 (4) with s=1; t=1
2. 64 + 2 6812 = 1933 (3) with s=1; t=1
3. 664 + 3 4192 = 3133 (2) with s=1; t=1
4. 3294 + 57 1122 = 2 4653 (1) with s=2; t=1
5. 4374 + 72 321 3922 = 173 5853 (1) with s=4; t=1
6. 7324 + 162 3412 = 6 7933 (3) with s=-1; t=2
7. 9494 + 6 858 6322 = 36 3053 (1) with s=-1; t=2
8. 1 0894 + 1 549 0342 = 15 6133 (4) with s=1; t=3
9. 2 2924 + 5 855 0412 = 39 5533 (2) with s=-1; t=2
10. 3 0074 + 1 361 154 1682 = 1 228 2253 (1) with s=-2; t=3
11. 4 3024 + 6 426 1992 = 72 6733 (3) with s=-3; t=1
12. 4 6654 + 25 660 3942 = 104 2213 (4) with s=5; t=1
13. 6 4444 + 142 946 2612 = 280 8733 (3) with s=-3; t=2
14. 8 5954 + 511 477 2462 = 643 9813 (4) with s=5; t=3
15. 14 0554 + 809 464 9222 = 885 4693 (4) with s=1; t=5
16. 17 4784 + 887 120 1012 = 958 3933 (2) with s=-1; t=3
17. 18 3904 + 86 484 8532 = 495 7693 (2) with s=-5; t=1
18. 24 5044 + 969 628 6992 = 1 091 5933 (3) with s=-1; t=4
19. 25 1794 + 1 658 732 3542 = 1 466 4133 (4) with s=7; t=1
20. 25 9804 + 2 984 101 4872 = 2 107 4893 (2) with s=-5; t=2
21. 27 6154 + 76 852 186 6782 = 18 076 6693 (4) with s=7; t=5
22. 31 2304 + 30 853 386 8272 = 9 840 4093 (2) with s=-5; t=3
23. 38 1474 + 2 783 083 1602 = 2 144 5613 (1) with s=5; t=2
24. 56 1304 + 6 126 744 4392 = 3 620 6413 (3) with s=-5; t=1
25. 56 2324 + 9 315 824 0212 = 4 591 2733 (3) with s=-3; t=4
26. 59 9634 + 77 170 270 4082 = 18 139 0253 (1) with s=7; t=2
27. 67 9774 + 4 631 366 5662 = 3 498 0133 (4) with s=7; t=3
28. 69 1014 + 5 268 182 8322 = 3 697 5853 (1) with s=-4; t=3
29. 73 7044 + 28 679 500 8012 = 9 480 1933 (2) with s=-1; t=4
30. 74 9104 + 15 005 507 5272 = 6 355 0093 (3) with s=-1; t=5
31. 75 6214 + 46 500 296 3542 = 12 996 0133 (4) with s=1; t=7
32. 98 8334 + 12 580 132 0482 = 6 330 3053 (1) with s=-1; t=4
33. 100 3384 + 11 547 018 1812 = 6 168 3133 (2) with s=-7; t=1
34. 102 1204 + 176 015 101 3012 = 31 444 2013 (3) with s=-5; t=4
35. 108 6604 + 1 086 380 9812 = 5 199 7213 (3) with s=-5; t=2
36. 120 0294 + 865 867 399 7602 = 90 853 3613 (1) with s=-4; t=5
37. 180 0544 + 245 010 210 2992 = 39 382 3933 (2) with s=-7; t=3
38. 185 5564 + 25 598 259 3592 = 12 255 5533 (2) with s=-7; t=2
39. 197 8514 + 110 567 251 1682 = 23 961 4253 (1) with s=8; t=1
40. 203 1304 + 39 350 943 5932 = 14 814 0493 (3) with s=-3; t=5
41. 224 9704 + 420 018 502 5012 = 56 355 0013 (2) with s=-1; t=5
42. 241 5274 + 389 650 312 3942 = 53 743 4533 (4) with s=11; t=1
43. 265 7074 + 951 601 494 9142 = 96 924 0133 (4) with s=1; t=9
44. 293 6404 + 205 006 750 1272 = 36 707 8093 (2) with s=-5; t=4
45. 302 3584 + 366 862 367 7192 = 52 286 5933 (3) with s=-7; t=1
46. 303 4394 + 308 948 386 1202 = 47 015 6813 (1) with s=-2; t=5
47. 311 7834 + 150 528 786 3202 = 31 783 8413 (1) with s=-5; t=4
48. 345 3454 + 98 622 932 8062 = 28 825 0213 (4) with s=5; t=7
49. 403 2424 + 876 708 083 7192 = 92 640 1933 (3) with s=-1; t=7
50. 504 4134 + 685 920 251 8082 = 81 191 6653 (1) with s=8; t=3
51. 599 6764 + 263 164 064 0592 = 58 341 1933 (3) with s=-7; t=2
52. 712 7014 + 173 871 144 6742 = 66 056 6533 (4) with s=11; t=3
53. 912 4794 + 29 744 433 4882 = 88 541 8253 (1) with s=7; t=4
54. 1 179 4864 + 127 495 184 5992 = 124 968 6733 (3) with s=-3; t=7
55. 1 286 4154 + 77 304 016 4862 = 140 009 3413 (4) with s=5; t=9

## Formulas

### Formula 1:

• a = (s2 + 3t2) (s4 - 18s2t2 + 9t4)
• b = 4st(s2 - 3t2) (s4 + 6s2t2 + 81t4) (3s4 + 2s2t2 + 3t4)
• c = (s4 - 2s2t2 + 9t4) (s4 + 30s2t2 + 9t4)

### Formula 2:

• a = 6st(s4 - 12t4)
• b = (s4 + 12t4) (s8 - 408s4t4 + 144t8)
• c = s8 + 168s4t4 + 144t8

### Formula 3:

• a = 6st(3s4 - 4t4)
• b = (3s4 + 4t4) (9s8 - 408s4t4 + 16t8)
• c = 9s8 + 168s4t4 + 16t8

### Formula 4:

• a = (3/2)st(s4 - 3t4)
• b = (1/8) (s4 + 3t4) (s8 - 102s4t4 + 9t8)
• c = (1/4) (s8 + 42s4t4 + 9t8)

Last updated February 25th, 2011