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Mixed square (Posted on 2021-06-18)

Find all positive integers n such that (n² + 11n - 4)n! + 33*13ⁿ + 4 is a perfect square.

No Solution Yet Submitted by Danish Ahmed Khan

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partial answer

| Comment 1 of 5

When n=1, f(n) equals 21^2.

When n=2, f(n) equals 75^2.

In my computer run, testing any n larger than 168 led to a crashed program due to OverflowError.

So, 1 and 2 are solutions, beyond that I am not sure, but apparently no solutions for 2 < n < 169

Posted by Larry on 2021-06-18 12:47:26

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