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## Homework Statement

Show that for all integers n>2, n does not divide n^2+2.

**2. The attempt at a solution**

I believe this solution can be solved by induction, I just don't know how to phrase it recursively.

For all n>2, n^2+2 mod n ≠ 0

Base case n=3

3^2 + 2 =11

11 mod 3 = 2 ≠ 0.

Show that

(n-1)^2 +2 mod n-1 ≠ 0