Divisibility

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Can you create a Latin Square from multiples of a six digit number?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

Is there an efficient way to work out how many factors a large number has?

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.