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The integral 1/(2pi(n+1))int_(-pi)^pif(x){(sin[1/2(n+1)x])/(sin(1/2x))}^2dx which gives the nth Cesàro mean of the Fourier series of f(x).

Any nondegenerate closed space curve may be nondegenerately deformed into either of the two curves illustrated above. Neither of these can be nondegenerately transformed into ...

A partial order defined by (i-1, i), (i+1, i) for odd i.

A number of the form 2^n-1 obtained by setting x=1 in a Fermat-Lucas polynomial, more commonly known as a Mersenne number.

The w-polynomials obtained by setting p(x)=3x and q(x)=-2 in the Lucas polynomial sequence. Setting f_n(1)=f_n (1) give a Fermat-Lucas number. The first few Fermat-Lucas ...

The compositeness test consisting of the application of Fermat's little theorem.

A plane curve of the form y=x^n. For n>0, the curve is a generalized parabola; for n<0 it is a generalized hyperbola.

The only whole number solution to the Diophantine equation y^3=x^2+2 is y=3, x=+/-5. This theorem was offered as a problem by Fermat, who suppressed his own proof.

The Diophantine equation x^n+y^n=z^n. The assertion that this equation has no nontrivial solutions for n>2 has a long and fascinating history and is known as Fermat's last ...

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) = ...