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A natural number n>3 such that n|(a^(n-2)-a) whenever (a,n)=1 (a and n are relatively prime) and a<=n. (Here, n|m means that n divides m.) There are an infinite number of ...

A divisor, also called a factor, of a number n is a number d which divides n (written d|n). For integers, only positive divisors are usually considered, though obviously the ...

Many algorithms have been devised for determining the prime factors of a given number (a process called prime factorization). They vary quite a bit in sophistication and ...

The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...

The Smarandache function mu(n) is the function first considered by Lucas (1883), Neuberg (1887), and Kempner (1918) and subsequently rediscovered by Smarandache (1980) that ...

A friend of a number n is another number m such that (m,n) is a friendly pair.

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...

Division by zero is the operation of taking the quotient of any number x and 0, i.e., x/0. The uniqueness of division breaks down when dividing by zero, since the product ...

A prime which does not divide the class number h(p) of the cyclotomic field obtained by adjoining a primitive pth root of unity to the field of rationals. A prime p is ...

The set of natural numbers (the positive integers Z-+ 1, 2, 3, ...; OEIS A000027), denoted N, also called the whole numbers. Like whole numbers, there is no general agreement ...