## If $$p$$ and $$n$$ are positive integers and $$p > n,$$ what is the remainder when $$p^2 - n^2$$ is divided by $$15?$$

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### If $$p$$ and $$n$$ are positive integers and $$p > n,$$ what is the remainder when $$p^2 - n^2$$ is divided by $$15?$$

by Vincen » Thu Apr 15, 2021 10:51 am

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If $$p$$ and $$n$$ are positive integers and $$p > n,$$ what is the remainder when $$p^2 - n^2$$ is divided by $$15?$$

(1) The remainder when $$p + n$$ is divided by $$5$$ is $$1.$$
(2) The remainder when $$p - n$$ is divided by $$3$$ is $$1.$$