Question

prove that 9^(n+2) - 4^n is divisible by 5 for all n>=1

Answer 1

are you familiar with Mathematical Induction?

Answer 2

yes i have made some exercises

Answer 3

Firstly prove that it's true for n=1
Then assume it's true for P(n)
After which you prove for P(n+1)

Answer 4

so i have to assume that the property is true for n and than to prove that is true for n+1?

Answer 5

Yes, that's the way Maths Induction works.
When you work out an expression for P(n+1) it should incorporate P(n)

Answer 6

\[9^{n+3}-4^{n+1}=5p\]

Answer 7

i have to prove that this property is true?

Answer 8

Yes you have to prove that is true with the assumption that 9^(n+2) - 4^n = 5k is true.

Answer 9

expand (4+5)^n and work on