Purr-fection

What is the smallest perfect square that ends with the four digits 9009?

More Mods

What is the units digit for the number 123^(456) ?

Old Nuts

In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?

Obviously?

Age 14 to 18 Challenge Level:

Consider separately when $N = 1^n + 8^n - 3^n - 6^n$ is divisible by $2$ and when it is divisible by $3$.