### 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?

### Euler's Officers

How many different ways can you arrange the officers in a square?

# Mod 3

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

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