# Thread: Prove by induction #2

1. ## Prove by induction #2

Prove by induction:
6*7^(n power) - 2*3^(n power) is divisible by 4, for all n is great than or equal to 1

2. Originally Posted by sderosa518
Prove by induction:
6*7^(n power) - 2*3^(n power) is divisible by 4, for all n is great than or equal to 1

6*7^n - 2*3^n = 2*[3*7^n - 3^n] , and since the expression in the parentheses is odd this number is 2*2* something else, and we're done
without any induction at all.

Of course, you can try induction as well...

Tonio

3. Originally Posted by tonio
6*7^n - 2*3^n = 2*[3*7^n - 3^n] , and since the expression in the parentheses is odd this number is 2*2* something else, and we're done
without any induction at all.

Of course, you can try induction as well...

Tonio
I assume you meant that the expression in the parentheses is even! since $3*7^n$ and $3^n$ are odd numbers, and subtracting two odd numbers gives an even number.

To solve by induction, simply follow the steps provided in the other topics you posted..