Challenge Level

Can you show that $n^5-n^3$ is always divisible by $24$?

Challenge Level

What is the remainder if you divide a square number by $8$?

Challenge Level

Can you find the smallest integer which has exactly 426 proper factors?

Challenge Level

Which numbers can you write as a difference of two squares? In how many ways can you write $pq$ as a difference of two squares if $p$ and $q$ are prime?