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p^x is an infinitary divisor of p^y (with y>0) if p^x|_(y-1)p^y, where d|_kn denotes a k-ary Divisor (Guy 1994, p. 54). Infinitary divisors therefore generalize the concept ...

A generalization by Kronecker of Kummer's theory of prime ideal factors. A divisor on a full subcategory C of mod(A) is an additive mapping chi on C with values in a ...

If f(x) is a nonconstant integer polynomial and c is an integer such that f(c) is divisible by the prime p, that p is called a prime divisor of the polynomial f(x) (Nagell ...

The extended greatest common divisor of two integers m and n can be defined as the greatest common divisor GCD(m,n) of m and n which also satisfies the constraint ...

There are two different statements, each separately known as the greatest common divisor theorem. 1. Given positive integers m and n, it is possible to choose integers x 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 ...

nu(x) = int_0^infty(x^tdt)/(Gamma(t+1)) (1) nu(x,alpha) = int_0^infty(x^(alpha+t)dt)/(Gamma(alpha+t+1)), (2) where Gamma(z) is the gamma function (Erdélyi et al. 1981, p. ...

As first shown by Meyer and Ritchie (1967), do-loops (which have a fixed iteration limit) are a special case of while-loops. A function that can be implemented using only ...

Given an amicable pair (m,n), the quantity sigma(m) = sigma(n) (1) = =s(m)+s(n) (2) = m+n (3) is called the pair sum, where sigma(n) is the divisor function and s(n) is the ...

The Dedekind psi-function is defined by the divisor product psi(n)=nproduct_(p|n)(1+1/p), (1) where the product is over the distinct prime factors of n, with the special case ...