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?

Lastly - Well

Stage: 3 Challenge Level:

How can you simplify this so that it does not contain a power
raised to a power?

Can you find a pattern in the last two digits? How about
starting with some simple cases?