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An almost integer is a number that is very close to an integer. Near-solutions to Fermat's last theorem provide a number of high-profile almost integers. In the season 7, ...

A cubic number is a figurate number of the form n^3 with n a positive integer. The first few are 1, 8, 27, 64, 125, 216, 343, ... (OEIS A000578). The protagonist Christopher ...

If p divides the numerator of the Bernoulli number B_(2k) for 0<2k<p-1, then (p,2k) is called an irregular pair. For p<30000, the irregular pairs of various forms are p=16843 ...

In order to find integers x and y such that x^2=y^2 (mod n) (1) (a modified form of Fermat's factorization method), in which case there is a 50% chance that GCD(n,x-y) is a ...

The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of ...

An algorithm similar to Neville's algorithm for constructing the Lagrange interpolating polynomial. Let f(x|x_0,x_1,...,x_k) be the unique polynomial of kth polynomial order ...

An n-bridge knot is a knot with bridge number n. The set of 2-bridge knots is identical to the set of rational knots. If L is a 2-bridge knot, then the BLM/Ho polynomial Q ...

Let j_k(alpha) denote the number of cycles of length k for a permutation alpha expressed as a product of disjoint cycles. The cycle index Z(X) of a permutation group X of ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), define the Hilbert function of M as the map ...

The expected number of real zeros E_n of a random polynomial of degree n if the coefficients are independent and distributed normally is given by E_n = ...