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A pair of primes (p,q) that sum to an even integer 2n=p+q are known as a Goldbach partition (Oliveira e Silva). Letting r(2n) denote the number of Goldbach partitions of 2n ...

A magic square is a square array of numbers consisting of the distinct positive integers 1, 2, ..., n^2 arranged such that the sum of the n numbers in any horizontal, ...

Marion's theorem (Mathematics Teacher 1993, Maushard 1994, Morgan 1994) states that the area of the central hexagonal region determined by trisection of each side of a ...

The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data's mean. For a sample size N, the mean ...

A function f is said to be an entire modular form of weight k if it satisfies 1. f is analytic in the upper half-plane H, 2. f((atau+b)/(ctau+d))=(ctau+d)^kf(tau) whenever [a ...

An NSW number (named after Newman, Shanks, and Williams) is an integer m that solves the Diophantine equation 2n^2=m^2+1. (1) In other words, the NSW numbers m index the ...

In the technical combinatorial sense, an a-ary necklace of length n is a string of n characters, each of a possible types. Rotation is ignored, in the sense that b_1b_2...b_n ...

Dickson states "In a letter to Tanner [L'intermediaire des math., 2, 1895, 317] Lucas stated that Mersenne (1644, 1647) implied that a necessary and sufficient condition that ...

An extremely fast factorization method developed by Pollard which was used to factor the RSA-130 number. This method is the most powerful known for factoring general numbers, ...

P(n), sometimes also denoted p(n) (Abramowitz and Stegun 1972, p. 825; Comtet 1974, p. 94; Hardy and Wright 1979, p. 273; Conway and Guy 1996, p. 94; Andrews 1998, p. 1), ...