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# Post 16 Students' Solutions

### Square Remainders

### Divisible Factorisations

### Proper Factors

### Square Difference

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Take a look at these recently solved problems.

Age 16 to 18

Challenge Level

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

Age 16 to 18

Challenge Level

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

Age 16 to 18

Challenge Level

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

Age 16 to 18

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?