Question 98
Show that for every prime natural number $p$ there exist natural numbers $x, y, z$ and $t$, not all zero, such that $t \lt p$ and
$$
x^{2} + y^{2} + z^{2} = t p
$$
$$
x^{2} + y^{2} + z^{2} = t p
$$
MathNet 2022-part-01 — 197 problems (EN–VI) Question 98
Math Olympiad Vault · MathNet 2022-part-01 — 197 problems (EN–VI)