Review question

# Can we write 33127 as the difference of two squares? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6171

## Question

Find the integer, $n$, that satisfies $n^2<33127<(n+1)^2$. Find also a small integer $m$ such that $(n+m)^2-33127$ is a perfect square. Hence express $33127$ in the form $pq$, where $p$ and $q$ are integers greater than $1$.

By considering the possible factorisations of $33127$, show that there are exactly two positive values of $m$ for which $(n+m)^2-33127$ is a perfect square, and find the other value.