Question 914045
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