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Sum of four cubes

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This applet finds the decomposition of any integer number not congruent to 4 or 5 (mod 9) into a sum of four cubes.

The applet uses the following formulas:

If n = 164, 596, 1892, 2324, 2756, 4052, 4484 (mod 6480) the following formula is used:

54x + 2 = (29484x2 + 2211x + 43)3 + (-29484x2 - 2157x - 41)3 + (9828x2 + 485x + 4)3 + (-9828x2 - 971x - 22)3

If n = 254, 902, 1442, 1874, 1982, 2414, 3062, 3494, 3602, 4034, 4142, 5114, 5222, 5654, 5762, 6302 (mod 6480) a method due to Demjanenko is used. Notice that the results can have hundreds of digits in this case.

In the remaining cases the number n is replaced by -n and then all solutions are multiplied by -1.

If you find any error or you have a comment, please fill in the form.

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