Find a proper positive factor of 48 and a proper positive multiple of 48 which add up to a perfect square. Can you prove that there are infinitely many such pairs?

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Solution

Take 16 as a factor of 48 and 48k as a multiple of 48.

Let k = n(3n + 2), n = 1, 2, 3…

Hence, there are infinitely many such pairs.

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