### N000ughty Thoughts

How many noughts are at the end of these giant numbers?

### Mod 3

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

### Common Divisor

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

# For What?

##### Age 14 to 16 Challenge Level:

Prove that if the integer $n$ is divisible by $4$ then it can be written as the difference of two squares.