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A p-adic number is an extension of the field of rationals such that congruences modulo powers of a fixed prime p are related to proximity in the so called "p-adic metric." ...

The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, ...

An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor ...

Machin-like formulas have the form mcot^(-1)u+ncot^(-1)v=1/4kpi, (1) where u, v, and k are positive integers and m and n are nonnegative integers. Some such formulas can be ...

A modulo multiplication group is a finite group M_m of residue classes prime to m under multiplication mod m. M_m is Abelian of group order phi(m), where phi(m) is the ...

Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and ...

A function tau(n) related to the divisor function sigma_k(n), also sometimes called Ramanujan's tau function. It is defined via the Fourier series of the modular discriminant ...

The biconjugate gradient stabilized (BCGSTAB) method was developed to solve nonsymmetric linear systems while avoiding the often irregular convergence patterns of the ...

Euler conjectured that at least n nth powers are required for n>2 to provide a sum that is itself an nth power. The conjecture was disproved by Lander and Parkin (1967) with ...

The Grassmannian Gr(n,k) is the set of k-dimensional subspaces in an n-dimensional vector space. For example, the set of lines Gr(n+1,1) is projective space. The real ...