Prove that the square of an odd number is always 1 more than a multiple of 4

Let n be any whole number. Any odd number can be written as 2n+1. Any odd number squared is therefore (2n+2)²=2n2n+22n+1=4n²+4n+1=4(n²+n)+1. n²+n is a whole number, so 4(n²+1) is a multiple of 4. Therefore, any odd number squared is 1 more than a multiple of 4.