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A Proth number is a number of the form N=k·2^n+1 for odd k, n a positive integer, and 2^n>k. The 2^n>k condition is needed since otherwise, every odd number >1 would be a ...

A mathematical problem, usually not requiring advanced mathematics, to which a solution is desired. Puzzles frequently require the rearrangement of existing pieces (e.g., 15 ...

The quaternion group is one of the two non-Abelian groups of the five total finite groups of order 8. It is formed by the quaternions +/-1, +/-i, +/-j, and +/-k , denoted Q_8 ...

The ramp function is defined by R(x) = xH(x) (1) = int_(-infty)^xH(x^')dx^' (2) = int_(-infty)^inftyH(x^')H(x-x^')dx^' (3) = H(x)*H(x), (4) where H(x) is the Heaviside step ...

A random permutation is a permutation containing a fixed number n of a random selection from a given set of elements. There are two main algorithms for constructing random ...

A set S of integers is said to be recursive if there is a total recursive function f(x) such that f(x)=1 for x in S and f(x)=0 for x not in S. Any recursive set is also ...

A regular ring in the sense of commutative algebra is a commutative unit ring such that all its localizations at prime ideals are regular local rings. In contrast, a von ...

A balanced incomplete block design (B,V) is called resolvable if there exists a partition R of its set of blocks B into parallel classes, each of which in turn partitions the ...

A configuration of 12 planes and 12 points such that six points lie in every plane and six planes pass through every point. Alternatively, the configuration consists of 16 ...

If A is a class of recursively enumerable sets, then the set of Gödel numbers of functions whose domains belong to A is called its index set. If the index set of A is a ...