Where do I start?

  • Thread starter recon
  • Start date
  • #1
399
1

Main Question or Discussion Point

Can someone point me in the right direction of solving the following problem:

Prove that for any postive integer n, the value of the expression [tex]3^{2n+2} - 8n -9[/tex] is divisible by 64.
 
Last edited:

Answers and Replies

  • #2
honestrosewater
Gold Member
2,105
5
I find when you're asked to prove that every member of some subset of the natural numbers has some property, induction usually works.
 
  • #3
matt grime
Science Advisor
Homework Helper
9,395
3
9^{n+1}-8n-9

or equivalently

9^n-8n-1

what is the binomial expansion of 9^n when considering 9=8+1?
 
  • #4
honestrosewater
Gold Member
2,105
5
Maybe I'm having a blonde moment, but doesn't [itex]a^{n + 1} - a = a(a^{n} - 1)[/itex], making [itex]9^{n + 1} - 9 - 8n = 9(9^{n} - 1) - 8n[/itex]?
 
  • #5
matt grime
Science Advisor
Homework Helper
9,395
3
ah, perhaps i ought to have been clearer: i wasn't say the epxressions are equal, but that if you prove one is divisible by 64 for all n, the other will be divislbe by 64 for all n (give or take a case when n=0). I let m=n+1 in the first, then relabelled n=m.
 
  • #6
399
1
I get it now. Thank you.
 

Related Threads for: Where do I start?

Replies
3
Views
614
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
2
Views
1K
Replies
4
Views
1K
Replies
9
Views
2K
Replies
2
Views
1K
Replies
22
Views
31K
Top