How many noughts are at the end of these giant numbers?
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
Find the largest integer which divides every member of the
following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
What is the largest number which, when divided into each of
$1905$, $2587$, $3951$, $7020$ and $8725$, leaves the same
remainder each time?