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A number that is both a square and a cube

numberspowersprime-factors

What is the smallest whole number greater than 1 that is both a perfect square and a perfect cube? Describe all numbers with this property in terms of their prime factorisations, and say how many of them lie below one million.

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Look at the prime factorisation. A square has all exponents even; a cube has all exponents multiples of 3.

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