Math CentralQuandaries & Queries


Question from Jolyn

Find the smallest possible value of a whole number m if 648x m is a perfect square

Hi Jolyn,

I can help some.

If a positive integer $n$ is a square then each of its prime factors divides $n$ an even number of times. For example 25 is a square and $25 = 5^{2}.$ Also $144$ is a square and $144 = 2^4 \times 3^{2}.$

The converse is also true, if each of the prime factors of $n$ divides $n$ an even number of times

then $n$ is a square.

I hope this helps,


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