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.

Answered by Rebecca R. Maths tutor

2784 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Prove that the sum of four consecutive whole numbers will always be even.


How do you simplify (3x-3)/(x-1)?


Which of these shapes has the most sides? Hexagon, Octagon, Rhombus, Trapezium


Work out 2 and 3/4 x 1 and 5/7 Give your answer as a mixed number in its simplest form.


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