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

An odd number can be expressed by the formula "2n + 1" where n stands for any integer. Therefore, the square of any odd number can be expressed as:(2n+1)^2 = (2n+1)(2n+1) = 4n^2 + 4n + 1 = 4(n^2 + n) + 1As 4(n^2 + n) is necessarily a multiple of 4, it is therefore clear that 4(n^2 + n) + 1 is 1 more than a multiple of four. Therefore the square of any odd number is 1 more than a multiple of 4