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The Legendre differential equation is the second-order ordinary differential equation (1-x^2)(d^2y)/(dx^2)-2x(dy)/(dx)+l(l+1)y=0, (1) which can be rewritten ...

Macdonald's plane partition conjecture proposes a formula for the number of cyclically symmetric plane partitions (CSPPs) of a given integer whose Ferrers diagrams fit inside ...

An elliptic curve of the form y^2=x^3+n for n an integer. This equation has a finite number of solutions in integers for all nonzero n. If (x,y) is a solution, it therefore ...

An element B of a ring is nilpotent if there exists a positive integer k for which B^k=0.

A quantity which is either 0 (zero) or positive, i.e., >=0.

A sieving procedure that can be used in conjunction with Dixon's factorization method to factor large numbers n. Pick values of r given by r=|_sqrt(n)_|+k, (1) where k=1, 2, ...

The rascal triangle is a number triangle with numbers arranged in staggered rows such that a_(n,r)=n(r-n)+1. (1) The published study of this triangle seems to have originated ...

The least positive integer m^* with the property that chi(y)=1 whenever y=1 (mod m^*) and (y,m)=1.

Set covering deployment (sometimes written "set-covering deployment" and abbreviated SCDP for "set covering deployment problem") seeks an optimal stationing of troops in a ...

The Struve function, denoted H_n(z) or occasionally H_n(z), is defined as H_nu(z)=(1/2z)^(nu+1)sum_(k=0)^infty((-1)^k(1/2z)^(2k))/(Gamma(k+3/2)Gamma(k+nu+3/2)), (1) where ...