### 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.

### A Biggy

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.

# Common Divisor

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

Find the largest integer which divides every member of the following sequence:

$$1^5-1,\ 2^5-2,\ 3^5-3,\cdots\ n^5-n.$$