You are given that n is a positive integer. By expressing (x^2n)-1 as a product of factors, prove that (2^2n)-1 is divisible by 3.

X2n-1 = (xn+1)(xn-1) Therefore we can say 22n-1 = (2n+1)(2n-1) . As 2n is always even, a multiple of 3 is always either going to be 1 above or 1 below it, e.g. 3 is one below 4 and 9 is 1 above 8, therefore either (2n+1) or (2n-1) is going to be a multiple of 3, making the entire equation 22n-1 divisible by 3 as (2n+1) and (2n-1) are multiplied together, and they keep their factors.

Answered by Abraham L. Maths tutor

7769 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the equation of the tangent to the curve y=x^3 + 4x^2 - 2x - 3 where x = -4


Given a curve has the equation f'(x) = 18x^2-24x-6 and passes through the point (3,40), use integration to find f(x) giving each answer in its simplest form.


y = 4sin(x)cos(3x) . Evaluate dy/dx at the point x = pi.


How do I add up the integers from 1 to 1000 without going insane?


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