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

7875 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Show that x^2 +6x+ 11 can be written as (x+p)^2 +q


Consider the closed curve between 0 <= theta < 2pi given by r(theta) = 6 + alpha sin theta, where alpha is some real constant strictly between 0 and 6. The area in this closed curve is 97pi/2. Calculate the value of alpha.


Express (3+ i)(1 + 2i) as a complex number in the form a+bi where a and b are real numbers.


Differentiate x^3 − 3x^2 − 9x. Hence find the x-coordinates of the stationary points on the curve y = x^3 − 3x^2 − 9x


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