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.
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 $3$.