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The number 1. There are n nth roots of unity, known as the de Moivre numbers.

For any prime number p and any positive integer n, the p^n-rank r_(p^n)(G) of a finitely generated Abelian group G is the number of copies of the cyclic group Z_(p^n) ...

A number which does not divide another exactly. For instance, 4 and 5 are aliquant divisors of 6. A number which is not an aliquant divisor (i.e., one that does divide ...

A quantity which does not equal zero is said to be nonzero. A real nonzero number must be either positive or negative, and a complex nonzero number can have either real or ...

To define a recurring digital invariant of order k, compute the sum of the kth powers of the digits of a number n. If this number n^' is equal to the original number n, then ...

An algorithm for making tables of primes. Sequentially write down the integers from 2 to the highest number n you wish to include in the table. Cross out all numbers >2 which ...

A complex number z may be represented as z=x+iy=|z|e^(itheta), (1) where |z| is a positive real number called the complex modulus of z, and theta (sometimes also denoted phi) ...

If n>19, there exists a Poulet number between n and n^2. The theorem was proved in 1965.

sum_(n=0)^(infty)[(q)_infty-(q)_n] = g(q)+(q)_inftysum_(k=1)^(infty)(q^k)/(1-q^k) (1) = g(q)+(q)_inftyL(q) (2) = g(q)+(q)_infty(psi_q(1)+ln(1-q))/(lnq) (3) = ...

The set theory symbol (aleph) for the cardinal number of a well-orderable infinite set.