A natural number $n\ge5$ leaves the remainder $2$ when divided by $3$. Prove that the square of $n$ is not a sum of a prime number and a perfect square.
Source: Moldova 2000 Grade 7 P6
Tags: number theory
A natural number $n\ge5$ leaves the remainder $2$ when divided by $3$. Prove that the square of $n$ is not a sum of a prime number and a perfect square.