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Generalized Fermat Equation


A generalization of the equation whose solution is desired in Fermat's last theorem

 x^n+y^n=z^n

to

 x^n+y^n=cz^n

for x, y, z, and c positive constants, with trivial solutions having x=0, y=0, or z=0 being excluded.

n=1 is trivial to solve by taking x=y=c and z=2. n=2 is more difficult, but can be solved by noting that solutions exist for values of c which can be written as a sum of two squares, the first few of which are 1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 25, 26, ... (OEIS A001481).


See also

Fermat's Last Theorem, Square Number

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References

Finch, S. "On a Generalized Fermat-Wiles Equation." http://algo.inria.fr/csolve/fermat.pdf.Sloane, N. J. A. Sequence A001481/M0968 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Generalized Fermat Equation

Cite this as:

Weisstein, Eric W. "Generalized Fermat Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GeneralizedFermatEquation.html

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