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

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?

Find the remainder when 3^{2001} is divided by 7.

We wonder who can find and explain the shortest and neatest proof that

$5^{2n+1} + 11^{2n+1} + 17^{2n+1}$

is divisible by 33 for every non negative integer n .