Finding the Last Digit of 2009^2009

[Oster]

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.

 

[Dick]

What are the last digits of 2009^1, 2009^2, 2009^3 etc? Keep going until you see the pattern.

 

[micromass]

To simplify dick's post: it suffices to look at 9^1, 9^2, 9^3,..., do you see why?

 

[Dick]

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.

 

[Oster]

yes thank you, i see the pattern.