SOLUTION: Give proof that 9^n-7^n is divisable by 32 if n is an even number

SOLUTION: Give proof that 9^n-7^n is divisable by 32 if n is an even number

Algebra.Com

Question 956942: Give proof that 9^n-7^n is divisable by 32 if n is an even number
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Let's look at the general case,

As you see from these 5 cases, and are always factors for even powers of .
In this case,

So the product is always a factor that why it's always divisible by .

RELATED QUESTIONS
Give Proof that 9^n-7^n is divisible by 32 If n is an odd... (answered by Fombitz)

Give Proof that 9^n-7^n is divisible by... (answered by Fombitz)

the three digit number 2m3 is added to the number 326 to give the three digit.number... (answered by FrankM,ankor@dixie-net.com)

prove, using the direct method of proof, that if n is a natural number, n(n+1) is an even (answered by josgarithmetic,robertb)

Using direct proof, prove that if n is a natural number, then n(n+1) is... (answered by Theo)

What is the largest intger that n^3-n is divisable by k for all postive intgers... (answered by venugopalramana)

Prove that for any integer n, {{{ n(n^2-1)(n+2) }}} is divisible by 12. Below is my... (answered by ikleyn)

Write an indirect proof. If n/2 is an integer, then n is even. (answered by wgunther)

Prove: If n is an integer, then n^2 + n^3 is an even... (answered by jim_thompson5910)