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.
problem has two steps. Students may be familiar with
factorisation methods for finding divisors but in this situation
the numbers do not divide exactly but instead have a common
remainder - providing an opportunity for students to look for a
step which will allow them to apply something familiar in a new and