The Egyptians expressed all fractions as the sum of different unit
fractions. Here is a chance to explore how they could have written
Weekly Problem 44 - 2013
If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?
Look at the triangle above and check that the rule really does work.
Can you work out the next two rows?
Can you prove the pattern will continue?
What about the third and fourth diagonals?
Click here for a poster of this problem.