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In Moralia, the Greek biographer and philosopher Plutarch states "Chrysippus says that the number of compound propositions that can be made from only ten simple propositions ...

A connective in logic which yields true if all conditions are true, and false if any condition is false. A AND B is denoted A ^ B (Mendelson 1997, p. 12), A&B, A intersection ...

Integers (lambda,mu) for a and b that satisfy Bézout's identity lambdaa+mub=GCD(a,b) are called Bézout numbers. For integers a_1, ..., a_n, the Bézout numbers are a set of ...

Two integers n and m<n are (alpha,beta)-multiamicable if sigma(m)-m=alphan and sigma(n)-n=betam, where sigma(n) is the divisor function and alpha,beta are positive integers. ...

Two numbers are heterogeneous if their prime factors are distinct. For example, 6=2·3 and 24=2^3·3 are not heterogeneous since their factors are each (2, 3).

Two numbers are homogeneous if they have identical prime factors. An example of a homogeneous pair is (6, 72), both of which share prime factors 2 and 3: 6 = 2·3 (1) 72 = ...

For every k>=1, let C_k be the set of composite numbers n>k such that if 1<a<n, GCD(a,n)=1 (where GCD is the greatest common divisor), then a^(n-k)=1 (mod n). Special cases ...

A sequence of numbers alpha_n is said to be uncorrelated if it satisfies lim_(n->infty)1/(2n)sum_(m=-n)^nalpha_m^2=1 lim_(n->infty)1/(2n)sum_(m=-n)^nalpha_malpha_(k+m)=0 for ...

A sequence of uncorrelated numbers alpha_n developed by Wiener (1926-1927). The numbers are constructed by beginning with {1,-1}, (1) then forming the outer product with ...

Sociable numbers computed using the analog of the restricted divisor function s^*(n) in which only unitary divisors are included.