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

(2x-1)² = 4x²- 4x + 1= 4(x²-x)+1The part of the expression which is: 4(x²-x) indicates that the value is a multiple of 4. The number 1 is then added which means that the statement 'the square of an odd number is always 1 more than a multiple of 4' is correct.