Question 98
Let $n$ be a square-free positive even number, $k$ be an integer, $p$ be a prime number, satisfying $p \lt 2\sqrt{n}$, $p \nmid n$, $p \mid n + k^2$. Prove that $n$ can be written as $n = ab + bc + ca$, where $a, b, c$ are distinctive positive integers.