Number theory problem

  • Thread starter ehrenfest
  • Start date
  • #1
2,013
1

Homework Statement


http://math.stanford.edu/~vakil/putnam07/07putnam2.pdf

I am working on number 2.
So I want to find 2^70 + 3^70 mod 13.
I can use Fermat's Little Theorem to reduce the exponent to 10, but I do not know what to do next...


Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
morphism
Science Advisor
Homework Helper
2,015
4
2^2 = 4 and 3^2 = 9

and 4^5 + 9^5 = (4+9)*something.
 
  • #3
2,013
1
4^5 + 9^5 = (4+9)*something.
Is that true? Where does that come from?
 
  • #4
morphism
Science Advisor
Homework Helper
2,015
4
You know how there's a formula for a^n - b^n? Well, there's also one for a^n + b^n when n is odd. (a^n + b^n = a^n - (-b)^n.)
 
  • #5
2,013
1
I see. Thanks.
 

Related Threads on Number theory problem

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
722
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
0
Views
801
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
471
  • Last Post
Replies
4
Views
849
  • Last Post
Replies
3
Views
563
  • Last Post
Replies
1
Views
2K
Top