Let $\displaystyle p$ be a prime of the form $\displaystyle 4n+3$. Prove that there exists integers $\displaystyle a,b$ such that $\displaystyle 0 < a,b \leq p$ such that $\displaystyle p \mid (a^{2}+b^{2})$
Yeah, something makes me think that there are two mistakes in the statement of this problem! Because it is similar to the very interesting problem
which is not a trivial problem at all.Let $\displaystyle p$ be a prime of the form $\displaystyle 4n+1$. Show that there exist integers $\displaystyle 0<a,b<p$ such that $\displaystyle p|a^2+b^2$.