Question

Prove the following using a direct proof:

The sum of the squares of 4 consecutive integers is an even integer

Answer 1

Answer: A positive whole number multiplied by any whole number will remain positive. In the case of the squares of 4, it will always end in a 6 which is a positive number.

Explanation:

4^2= 16

16^2 = 256

256^2= 65,536

etc.