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In a 1631 edition of Academiae Algebrae, J. Faulhaber published the general formula for the power sum of the first n positive integers, sum_(k=1)^(n)k^p = H_(n,-p) (1) = ...

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 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 probability that two events will both happen is hk, where h is the probability that the first event will happen, and k is the probability that the second event will ...

In a given acute triangle DeltaABC, locate a point whose distances from A, B, and C have the smallest possible sum. The solution is the point from which each side subtends an ...