### More Mods

What is the units digit for the number 123^(456) ?

### N000ughty Thoughts

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

### Novemberish

a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.

# Mod 3

##### Stage: 4 Challenge Level:

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