Number theory !

  • Thread starter Oster
  • Start date
  • #1
85
0
1. What is the last digit of 2009^2009



I think you go about this by factoring 2009 as 7*7*41. I'm pretty much stuck.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,263
619
What are the last digits of 2009^1, 2009^2, 2009^3 etc? Keep going until you see the pattern.
 
  • #3
22,129
3,297
To simplify dick's post: it suffices to look at 9^1, 9^2, 9^3,..., do you see why?
 
  • #4
Dick
Science Advisor
Homework Helper
26,263
619
To simplify dick's post: it suffices to look at 9^1, 9^2, 9^3,..., do you see why?

And it's even easier than that if you know mod arithmetic and notice 2009 is equal to (-1) mod 10.
 
  • #5
85
0
yes thank you, i see the pattern.
 

Related Threads on Number theory !

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
742
  • Last Post
Replies
2
Views
993
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
833
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
2
Views
1K
Top