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A Diophantine problem (i.e., one whose solution must be given in terms of integers) which seeks a solution to the following problem. Given n men and a pile of coconuts, each ...

An algorithm which can be used to find integer relations between real numbers x_1, ..., x_n such that a_1x_1+a_2x_2+...+a_nx_n=0, with not all a_i=0. Although the algorithm ...

A prime magic square is a magic square consisting only of prime numbers (although the number 1 is sometimes allowed in such squares). The left square is the 3×3 prime magic ...

A prime constellation of four successive primes with minimal distance (p,p+2,p+6,p+8). The term was coined by Paul Stäckel (1892-1919; Tietze 1965, p. 19). The quadruplet (2, ...

Propositional calculus is the formal basis of logic dealing with the notion and usage of words such as "NOT," "OR," "AND," and "implies." Many systems of propositional ...

Let a number n be written in binary as n=(epsilon_kepsilon_(k-1)...epsilon_1epsilon_0)_2, (1) and define b_n=sum_(i=0)^(k-1)epsilon_iepsilon_(i+1) (2) as the number of digits ...

There are two related conjectures, each called the twin prime conjecture. The first version states that there are an infinite number of pairs of twin primes (Guy 1994, p. ...

A connective in logic known as the "exclusive or," or exclusive disjunction. It yields true if exactly one (but not both) of two conditions is true. The XOR operation does ...

Given three objects, each of which may be a point, line, or circle, draw a circle that is tangent to each. There are a total of ten cases. The two easiest involve three ...

Augmentation is the dual operation of truncation which replaces the faces of a polyhedron with pyramids of height h (where h may be positive, zero, or negative) having the ...