SOLUTION: What is the remainder when 3^10 is divided by 5? (Hint: Solve some simpler problems first and look for a pattern) Thanks if you choose to help me with this!

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: What is the remainder when 3^10 is divided by 5? (Hint: Solve some simpler problems first and look for a pattern) Thanks if you choose to help me with this!      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 983700: What is the remainder when 3^10 is divided by 5? (Hint: Solve some simpler problems first and look for a pattern)
Thanks if you choose to help me with this!
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
3%5E2%2F5=9%2F5=1%264%2F5
3%5E3%2F5=27%2F5=5%262%2F5
3%5E4%2F5=81%2F5=16%261%2F5
3%5E5%2F5=243%2F5=QandRemainderThreeFifth, r=3%2F5

Not sure I see a pattern, but there are only four possible remainders.

3%5E6%2F5=729%2Bremainder, r=4%2F5

Guess is if not too early, the patern is 4,2,1,3,repeating those four.
The first 4 starts at power=2.
Guessing further, that 3%5E10 will give r=4.