Prove by mathematical induction that 11^n-6 is divisible by 5 for all natural numbers n

First I would do the base case (the first value):Test n=1,111-6=5. 5 is divisible by 5 therefore true for n=1.
Now we assume true for n=k,11k-6 is divisible by 5.Next we test n=k+1,11k+1-6We can rearrange this into 1111k-6= 1011k+11k-6We know that for n=k the result is 11k-6 which we assume to be true so that part can be assumed to be true.The first part can be factorised into 5(2*11k) which is divisible by 5. Therefore we have shown that if true for n=k, true for n=k+1 and as we shown true for n=1 it must also be true for all natural numbers. So we have proved this through induction

Answered by Further Mathematics tutor

3621 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

How can we solve a limit having an indetermination of the type 0/0 or infinity divided by infinity?


How would you use the Integration Factor method to solve an ordinary first-order linear differential equation?


How far is the point (7,4,1) from the line that passes through the points (6,4,1) and (6,3,-1)?


Prove e^(ix) = cos (x) + isin(x)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2026 by IXL Learning