Question

Prove that the sum of the squares of two consecutive even numbers is a multiple of 4

Answer 1

Since the final answer has a factor of 4, it is a multiple of 4.

Explanation:

Let the smaller even number be 2n.

The next greater even number is 2n + 2.

(2n)² + (2n + 2)² = 4n² + 4n² + 8n + 4 = 8n² + 8n + 4 = 4(2n² + 2n + 1)