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The term "cylinder" has a number of related meanings. In its most general usage, the word "cylinder" refers to a solid bounded by a closed generalized cylinder (a.k.a. ...

The general bivariate quadratic curve can be written ax^2+2bxy+cy^2+2dx+2fy+g=0. (1) Define the following quantities: Delta = |a b d; b c f; d f g| (2) J = |a b; b c| (3) I = ...

As originally stated by Gould (1972), GCD{(n-1; k),(n; k-1),(n+1; k+1)} =GCD{(n-1; k-1),(n; k+1),(n+1; k)}, (1) where GCD is the greatest common divisor and (n; k) is a ...

An inverse function of an Abelian integral. Abelian functions have two variables and four periods, and can be defined by Theta(v,tau;q^'; ...

Let a^p+b^p=c^p be a solution to Fermat's last theorem. Then the corresponding Frey curve is y^2=x(x-a^p)(x+b^p). (1) Ribet (1990a) showed that such curves cannot be modular, ...

For elliptic curves over the rationals Q, the group of rational points is always finitely generated (i.e., there always exists a finite set of group generators). This theorem ...

The Ochoa curve is the elliptic curve 3Y^2=2X^3+386X^2+256X-58195, given in Weierstrass form as y^2=x^3-440067x+106074110. The complete set of 23 integer solutions (where ...

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 hundred-dollar, hundred-digits challenge problems are a set of ten problems in numerical analysis published in the January/February 2002 issue of SIAM News ...

A conjecture which treats the heights of points relative to a canonical class of a curve defined over the integers.