2016 AMC 10B Problems/Problem 8: Difference between revisions
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We notice that <math>2015^{n}</math> is 25 (mod 100) when n is even and 75 (mod 100) when n is odd. (check for yourself). Since 2016 is even, <math>2015^{2016}</math> is 25 (mod 100) and <math>2015^{2016}-2017 \equiv 25 - 17 \equiv 08 (mod 100)</math> | We notice that <math>2015^{n}</math> is 25 (mod 100) when n is even and 75 (mod 100) when n is odd. (check for yourself). Since 2016 is even, <math>2015^{2016}</math> is 25 (mod 100) and <math>2015^{2016}-2017 \equiv 25 - 17 \equiv 08 (mod 100)</math> | ||
So the answer is <math>\textbf{(A)}\ 0 \qquad</math> | So the answer is <math>\textbf{(A)}\ 0 \qquad</math> | ||
solution by Wwang | solution by Wwang | ||
Revision as of 09:49, 21 February 2016
Problem
What is the tens digit of 
Solution
We notice that 
is 25 (mod 100) when n is even and 75 (mod 100) when n is odd. (check for yourself). Since 2016 is even, 
is 25 (mod 100) and 
So the answer is 
solution by Wwang
