Prove that all Square Numbers are either a Multiple of 4, or 1 more than a Multiple of 4 

This video shows how to prove that all square numbers are either a multiple of 4, or 1 more than a multiple of 4. The proof uses the fact that all even numbers are multiples of 2 and so can be written as 2n, where n is a positive integer and also that any odd number can be obtained by adding 1 to the nearest even number and so can be written as 2n+1. This is an example of algebraic proof.