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

If we say n is any number, then we know 2n represents an even number - any number multiplied by 2 is always even. 2n+1 represents an odd number - adding 1 to an even number always gives an odd number (2n + 1)2 = (2n + 1)(2n + 1) = 4n2 + 2n + 2n + 1 = 4n2 + 4n + 1 = 4(n2 + n) + 1. Here 4(n2 + n) represents a multiple of four so we have a multiple of 4 plus 1. Hence the square of an odd number is always one more than a multiple of 4.

RR
Answered by Rebecca R. Maths tutor

2832 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Find the highest common factor of 432 and 522


Solve the simultaneous equations: 2x-3y = 16 x+2y= -6


A line joins 2 points (2,9) and (5,4). Calculate the gradient of the straight line and then write down the equation of the straight line.


When working with probabilities why is it sometimes necessary to add and sometimes to multiply?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences