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In a set X equipped with a binary operation · called a product, the multiplicative identity is an element e such that e·x=x·e=x for all x in X. It can be, for example, the ...

For any ideal I in a Dedekind ring, there is an ideal I_i such that II_i=z, (1) where z is a principal ideal, (i.e., an ideal of rank 1). Moreover, for a Dedekind ring with a ...

A class number formula is a finite series giving exactly the class number of a ring. For a ring of quadratic integers, the class number is denoted h(d), where d is the ...

A number n is called a k e-perfect number if sigma_e(n)=kn, where sigma_e(n) is the sum of the e-divisors of n.

Surreal numbers are the most natural collection of numbers which includes both the real numbers and the infinite ordinal numbers of Georg Cantor. They were invented by John ...

The portion of number theory concerned with expressing an integer as a sum of integers from some given set.

Analytic number theory is the branch of number theory which uses real and complex analysis to investigate various properties of integers and prime numbers. Examples of topics ...

A number n for which a shortest chain exists (which is also a Hansen chain) is called a Hansen number.

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

A polygonal number is a type of figurate number that is a generalization of triangular, square, etc., to an n-gon for n an arbitrary positive integer. The above diagrams ...