SOLUTION: Show that any integer N = 7 modulo 8 cannot be expressed as the sum of the squares of three integers.

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Question 366789: Show that any integer N = 7 modulo 8 cannot be expressed as the sum of the squares of three integers.
Answer by Sphinx pinastri(17) About Me  (Show Source):
You can put this solution on YOUR website!
Let's make a table of n^2 modulo 8 .
0^2 modulo 8 = 0
1^2 modulo 8 = 1
2^2 modulo 8 = 4
3^2 modulo 8 = 1
4^2 modulo 8 = 0
5^2 modulo 8 = 1
6^2 modulo 8 = 4
7^2 modulo 8 = 1
Exhaustive search shows that one cannot find 3 numbers whose sum
is 7 modulo 8.