N is a positive integer which is expressible as the sum of cubes of two positive integers.
Given that N is not divisible by 9, find the possible remainders when N is divided by 63.

(In reply to re: computer solution by broll)

Clearly,  both x^3 and (N-x)^3 are equal mod N.

The above applies as well to s= x1+x2 and ss=x1+x2+x3+  ...  xn.

Edited on November 10, 2016, 10:56 pm

Posted by Ady TZIDON on 2016-11-10 22:52:21