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The term "product" refers to the result of one or more multiplications. For example, the mathematical statement a×b=c would be read "a times b equals c," where a is called ...

Proper covers are defined as covers of a set X which do not contain the entire set X itself as a subset (Macula 1994). Of the five covers of {1,2}, namely {{1},{2}}, {{1,2}}, ...

Any ideal of a ring which is strictly smaller than the whole ring. For example, 2Z is a proper ideal of the ring of integers Z, since 1 not in 2Z. The ideal <X> of the ...

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 ...

The pseudosmarandache function Z(n) is the smallest integer such that sum_(k=1)^(Z(n))k=1/2Z(n)[Z(n)+1] is divisible by n. The values for n=1, 2, ... are 1, 3, 2, 7, 4, 3, 6, ...

The Pythagoras tree is a fractal constructed iteratively from a right triangle with squares erected on each of the sides. Subsequent iterations add additional similar right ...

Given a matrix A, its QR-decomposition is a matrix decomposition of the form A=QR, where R is an upper triangular matrix and Q is an orthogonal matrix, i.e., one satisfying ...

Let R be the class of expressions generated by 1. The rational numbers and the two real numbers pi and ln2, 2. The variable x, 3. The operations of addition, multiplication, ...

There exist infinitely many odd integers k such that k·2^n-1 is composite for every n>=1. Numbers k with this property are called Riesel numbers, while analogous numbers with ...

Given a map f:S->T between sets S and T, the map g:T->S is called a right inverse to f provided that f degreesg=id_T, that is, composing f with g from the right gives the ...