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Take a look at these recently solved problems.
What is the remainder if you divide a square number by $8$?
Can you show that $n^5-n^3$ is always divisible by $24$?
Can you find the smallest integer which has exactly 426 proper factors?
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?
Explore a new way of multiplying with matrices.
What happens when you find the powers of this matrix?