Question 85
Let $n$ be an odd positive integer greater than $3$. Let $k$ denote the least positive integer such that $kn+1$ is a perfect square and $l$ denote the least positive integer such that $ln$ is a perfect square.
Prove that $n$ is a prime number if and only if $k \gt \frac{1}{4}n$ and $l \gt \frac{1}{4}n$.
(V.I. Bernik, I.K. Zhuk, O.V. Melnikov, Collection of Problems in Math. Olympiads)
Prove that $n$ is a prime number if and only if $k \gt \frac{1}{4}n$ and $l \gt \frac{1}{4}n$.
(V.I. Bernik, I.K. Zhuk, O.V. Melnikov, Collection of Problems in Math. Olympiads)