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Fermat Polynomial


FermatPolynomial

The W-polynomials obtained by setting p(x)=3x and q(x)=-2 in the Lucas polynomial sequence. The first few Fermat polynomials are

F_1(x)=1
(1)
F_2(x)=3x
(2)
F_3(x)=9x^2-2
(3)
F_4(x)=27x^3-12x
(4)
F_5(x)=81x^4-54x^2+4,
(5)

The Fermat polynomials satisfy

 F_n(1)=F_n
(6)

where F_n are called Fermat numbers.


See also

Fermat-Lucas Polynomial, Lucas Polynomial Sequence

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Cite this as:

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

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