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For any M, there exists a t^' such that the sequence n^2+t^', where n=1, 2, ... contains at least M primes.

As first shown by Meyer and Ritchie (1967), do-loops (which have a fixed iteration limit) are a special case of while-loops. A function that can be implemented using only ...

The Paley graph of order q with q a prime power is a graph on q nodes with two nodes adjacent if their difference is a square in the finite field GF(q). This graph is ...

A map x|->x^p where p is a prime.

Let t(m) denote the set of the phi(m) numbers less than and relatively prime to m, where phi(n) is the totient function. Then if S_m=sum_(t(m))1/t, (1) then {S_m=0 (mod m^2) ...

A finite simple group of Lie-type. The following table summarizes the types of twisted Chevalley groups and their respective orders. In the table, q denotes a prime power and ...

The cube of a graph is defined as its third graph power.

Mills' theorem states that there exists a real constant A such that |_A^(3^n)_| is prime for all positive integers n (Mills 1947). While for each value of c>=2.106, there are ...

An exponent is the power p in an expression of the form a^p. The process of performing the operation of raising a base to a given power is known as exponentiation.

If an analytic function has a single simple pole at the radius of convergence of its power series, then the ratio of the coefficients of its power series converges to that ...