Exercise 2.1.6 (First examples, part 6)

Question

Prove that if $p$ is prime and $a^2 \equiv b^2 \pmod p$, then $\mid (a+b)$ or $p \mid (a-b)$.

Richard Ganaye · Accepted Answer

\begin{proof} Suppose that $p$ is prime and $a^2 \equiv b^2 \pmod p$.
Then $$p \mid (a^2 - b^2)= (a-b)(a+b).$$
Since $p$ is prime, $p \mid a +b$ or $p\mid a-b$.
\end{proof}

Exercise 2.1.6 (First examples, part 6)

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Exercise 2.1.6 (First examples, part 6)

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