Hi
Can you please help me solve the below question.
The difference between a prime number and a square number is 100. Which is larger?
Let's call the square number $n^2$ and the prime number $p$. Suppose $n^2>p$. Then, we know $n^2-100=p$. But, the left hand side factors to $(n+10)(n-10)$. Since $n^2$ is a perfect square, we know that $n$ is an integer, and so $n+10$ and $n-10$ are both integers. However, this implies that $p$ is a composite number, which is a contradiction. Therefore it must be that $p>n^2$.
Example: $p=101, n^2=1$.