# Difference between revisions of "2016 AMC 10B Problems/Problem 8"

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− | Notice that <math>2015^ | + | Notice that <math>2015^n</math> is congruent to <math>25\pmod{100}</math> when <math>n</math> is even and <math>75\pmod{100}</math> when <math>n</math> is odd. (Check for yourself). Since <math>2016</math> is even, <math>2015^{2016} \equiv 25\pmod{100}</math> and <math>2015^{2016}-2017 \equiv 25 - 17 \equiv \underline{0}8\pmod{100}</math>. |

− | So the answer is <math>\textbf{(A)}\ 0 | + | So the answer is <math>\textbf{(A)}\ 0</math>. |

solution by Wwang | solution by Wwang |

## Revision as of 10:37, 21 February 2016

## Problem

What is the tens digit of

## Solution

Notice that is congruent to when is even and when is odd. (Check for yourself). Since is even, and .

So the answer is .

solution by Wwang