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What is the smallest positive integer n n such that 1 + n + n 2 + n 3 + n 4 1 + n + n^2 + n^3 + n^4 is a perfect square?


The answer is 3.

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1 solution

Austin Li
May 29, 2020

If n=1 then 5 is not a perfect square. If n=2 then 31 is not a perfect square. If n=3 then 121 is a perfect square. Therefore, n=3. Plus, if n=0--- well, the problem says POSITIVE INTEGER so 0 is incorrect.

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