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An integer m such that if p|m, then p^2|m, is called a powerful number. There are an infinite number of powerful numbers, and the first few are 1, 4, 8, 9, 16, 25, 27, 32, ...

The factorization of a number into its constituent primes, also called prime decomposition. Given a positive integer n>=2, the prime factorization is written ...

A projective plane, sometimes called a twisted sphere (Henle 1994, p. 110), is a surface without boundary derived from a usual plane by addition of a line at infinity. Just ...

Two integers are relatively prime if they share no common positive factors (divisors) except 1. Using the notation (m,n) to denote the greatest common divisor, two integers m ...

A rooted tree is a tree in which a special ("labeled") node is singled out. This node is called the "root" or (less commonly) "eve" of the tree. Rooted trees are equivalent ...

The base-3 method of counting in which only the digits 0, 1, and 2 are used. Ternary numbers arise in a number of problems in mathematics, including some problems of ...

A trinomial coefficient is a coefficient of the trinomial triangle. Following the notation of Andrews (1990), the trinomial coefficient (n; k)_2, with n>=0 and -n<=k<=n, is ...

Abstract Algebra

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...