I recently found myself asking if the following (diophantine) expression ever evaluates to a square number:
I was surprised both to be unable to stumble across an integer value for $n$ that results in a square number, and then surprised not see an obvious, eloquent, proof showing why this expression can never be square.
I would be interested in any pointers to work on the question of if/when equations of the form:
$$ A + Bn = c^2 $$
have a (non-trivial) solution. I'm assuming the convention that capital variables are constants, while non-capitals are free variables.