Find all integer solutions for $a_1(a_1+k)(a_1+2k)...(a_1+(2k+1)d)+1 = n^2$ [closed]
Closed as not constructive by beloh on Dec 22, 2022 at 10:47
This question cannot be answered in a way that is helpful to anyone. It's not possible to learn something from possible answers, except for the solution for the specific problem of the asker.
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The initial observation is explained by the identity $$(x^2 + 3x + 1)^2 = x(x+1)(x+2)(x+3) + 1$$
The generalisation is messed up in the question as it currently stands, but the only smallish similar identity which I can find is the uninteresting $$(x+1)^2 = x(x+2) + 1$$
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