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Egyptian Fractions

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

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Weekly Problem 44 - 2013

Weekly Problem 44 - 2013

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Harmonic Triangle

Can you see how to build a harmonic triangle? Can you work out the next two rows?

Weekly Problem 26 - 2008

Stage: 3 and 4 Challenge Level: Challenge Level:1

As $n$ takes each positive integer value in turn (that is, $n=1$, $n=2$, $n=3$...) how many different values are obtained for the remainder when $n^2$ is divided by $n+4$?
 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

 

 

This problem is taken from the UKMT Mathematical Challenges.

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