Definition:Approximate Fermat Equation
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Definition
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.
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $729$