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The categorical notion which is dual to product. The coproduct of a family {X_i}_(i in I) of objects of a category is an object C=coproduct_(i in I)X_i, together with a ...

When referring to a planar object, "free" means that the object is regarded as capable of being picked up out of the plane and flipped over. As a result, mirror images are ...

The compositeness test consisting of the application of Fermat's little theorem.

1 and -1 are the only integers which divide every integer. They are therefore called the prime units.

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 ...

A deeper result than the Hardy-Ramanujan theorem. Let N(x,a,b) be the number of integers in [n,x] such that inequality a<=(omega(n)-lnlnn)/(sqrt(lnlnn))<=b (1) holds, where ...

The converse of Fermat's little theorem is also known as Lehmer's theorem. It states that, if an integer x is prime to m and x^(m-1)=1 (mod m) and there is no integer e<m-1 ...

Lucas's theorem states that if n>=3 be a squarefree integer and Phi_n(z) a cyclotomic polynomial, then Phi_n(z)=U_n^2(z)-(-1)^((n-1)/2)nzV_n^2(z), (1) where U_n(z) and V_n(z) ...

A nonzero and noninvertible element a of a ring R which generates a prime ideal. It can also be characterized by the condition that whenever a divides a product in R, a ...

In database structures, two quantities are generally of interest: the average number of comparisons required to 1. Find an existing random record, and 2. Insert a new random ...