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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.

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Factoring a Million

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

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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.