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Why 24?

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.

Factoring a Million

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?


Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

A Biggy

Age 14 to 16 Challenge Level:

Find the smallest positive integer $N$ such that \[{N\over 2} \] is a perfect cube, \[{N\over 3} \] is a perfect fifth power and \[{N\over 5} \] is a perfect seventh power.