Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
true?

Even So

Age 11 to 14 Challenge Level:

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?