SOLUTION: verify that if an integer is simultaneously a square and a cube , then it must be either of the form 7k or 7k+1

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Question 914045: verify that if an integer is simultaneously a square and a cube , then it must be either of the form 7k or 7k+1
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Integer n must be a sixth power of an integer.

We can check that all sixth powers are either 0 or 1 (mod 7)
0^6 = 0
1^6 = 1
2^6 = 64 = 1
3^6 = 729 = 1
4^6 = (-3)^6 = 3^6 = 1
5^6 = (-2)^6 = 2^6 = 1
6^6 = (-1)^6 = 1^6 = 1