Latest Maths Olympiad Aptitude Question SOLUTION: For how many integers n is n/(20-n) the square of an integer?

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For how many integers n is n/(20-n) the square of an integer?

Solution

We could assign k to be an integer such that n/(20-n) = k^2,
Solve for n and you will get n = 20-[20/(1+k^2)].
now possible values of k = 0,1,2,3, after that second part will become a fraction, This implies that k = {0,1,2,3} and n = 0, 10, 16, or 18.

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Asked In Maths Olympiad Sanjana Patnaik (12 years ago)

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