Definition:Approximate Fermat Equation

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An approximate Fermat equation is a Diophantine equation of the form:

$x^n = y^n + z^n \pm c$

such that $\dfrac {x^n} {y^n + z^n} \approx 1$.

That is, the numbers $x, y, z, n$ almost, but not quite, form a solution to:

$x^n = y^n + z^n$

and thus almost form a counterexample to Fermat's Last Theorem.