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63 Division Decision (Posted on 2016-11-10) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Hints/Tips re(2): computer solution - observation Comment 3 of 3 |
(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

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