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?

Mod 3

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

Novemberish

Stage: 4 Challenge Level:

(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 $100$.