- #1

- 39

- 0

## Homework Statement

Proof that if 32 -|- ((a^2+3)(a^2+7)) if a is even. (note: -|- means NOT divides)

The question asks for a proof of this statement.

## Homework Equations

If a | b, then there exists an integer k such that b = ka.

## The Attempt at a Solution

If the contrapositive of the statement is true, then so is the statement. So we will prove that if a is odd, then 32 | ((a^2+3)(a^2+7)).

Since a is odd, (a^2+3)(a^2+7) is even, 2 | ((a^2+3)(a^2+7)). This must mean that there exists an integer k such that ((a^2+3)(a^2+7)) = 2k. ...