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A Biggy

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.

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.

Fac-finding

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.

Factoring a Million

Age 14 to 16 Challenge Level:

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