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The length of a number n in base b is the number of digits in the base-b numeral for n, given by the formula L(n,b)=|_log_b(n)_|+1, where |_x_| is the floor function. The ...

Given a set S of n nonnegative integers, the number partitioning problem requires the division of S into two subsets such that the sums of number in each subset are as close ...

It is possible to construct simple functions which produce growing patterns. For example, the Baxter-Hickerson function f(n)=1/3(2·10^(5n)-10^(4n)+2·10^(3n)+10^(2n)+10^n+1) ...

Place 2n balls in a bag and number them 1 to 2n, then pick half of them at random. The number of different possible sums for n=1, 2, 3, ... are then 2, 5, 10, 17, 26, ... ...

A set of numbers obeying a pattern like the following: 91·37 = 3367 (1) 9901·3367 = 33336667 (2) 999001·333667 = 333333666667 (3) 99990001·33336667 = 3333333366666667 (4) 4^2 ...

The algebraic integers in a number field.

A number theoretic character, also called a Dirichlet character (because Dirichlet first introduced them in his famous proof that every arithmetic progression with relatively ...

A number theoretic function is a function whose domain is the set of positive integers.

Simplemindedly, a number theoretic transform is a generalization of a fast Fourier transform obtained by replacing e^(-2piik/N) with an nth primitive root of unity. This ...

Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and ...