Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

Maundy Money

Stage: 3 Short Challenge Level:

The total amount distributed was $2 \times 64 \times 64=2 \times 2^6 \times 2^6=2^{13}$.