Math CentralQuandaries & Queries


Question from Jerry, a student:

How would you prove that for any positive integer n, the value of the expression 3^(2n+2) - 8n -9 is divisible by 64.

Jerry, we have two responses for you:

Hi Jerry.

The only thing tricky about this problem is that you are given the form for (n+1). One easy way to begin your solution would be to write the term for n, noting that 3(2n) = 9n. Note that the given expression for n+1 is just 9 times the expression for n plus something. It is your job to determine that something.

Chris Fisher.



At the induction step write 3(2n+4) - 8(n+1) -9 as 

9×3(2n+2) - 9×8n + 8×8n - 9×9 + 64

and if you collect terms carefully you'll see the next step.


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS