Question

using mathematical induction show positive integers n
11^n-4n is divisible by 7​

Answer 1

Answer:

8

Down vote

Accepted

We have that 11≡4(mod7). Thus 11n≡4n(mod7),∀n∈N. That is, 11n−4n is divisible by 7.

If you want to use induction note that

11n+1−4n+1=(7+4)⋅11n−4⋅4n=7⋅11n+4⋅(11n−4n).

Now 7⋅11n and 11n−4n are multiples of 7 (the second one using the induction hypothesis)