His most impressive work in number theory is on amicable numbers.

In mathematics, Thabit discovered an equation for determining amicable numbers.

Amicable numbers were known to the Pythagoreans, who credited them with many mystical properties.

A pair of amicable numbers constitutes an aliquot sequence of period 2.

(Sometimes the term sociable number is used to encompass amicable numbers as well.)

A pair of amicable numbers is a set of sociable numbers of order 2.

In 1955, Paul Erdős showed that the density of amicable numbers, relative to the positive integers, was 0.

Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number.

It is not known whether a pair of coprime amicable numbers exists, though if any does, the product of the two must be greater than 10.

Sociable numbers are generalizations of the concepts of amicable numbers and perfect numbers.

Fermat and Descartes also rediscovered pairs of amicable numbers known to Arab mathematicians.

Amenable numbers should not be confused with amicable numbers, which are pairs of integers whose divisors add up to each other.

Amicable numbers are featured briefly in the novel The Stranger House by Reginald Hill.

Studied a slight variant of Thabit ibn Qurra's theorem on amicable numbers.

While these rules do generate some pairs of amicable numbers, many other pairs are known, so these rules are by no means comprehensive.

Also, a pair of coprime amicable numbers cannot be generated by Thabit's formula (above), nor by any similar formula.

When both n and n-1 yield prime Thabit numbers, and is also prime, a pair of amicable numbers can be calculated as follows:

Borho does research on representation theory, Lie algebras, ring theory and also on number theory (amicable numbers) and tilings.

In number theory, Fermat studied Pell's equation, perfect numbers, amicable numbers and what would later become Fermat numbers.

R Rashed, Materials for the study of the history of amicable numbers and combinatorial analysis (Arabic), J. Hist.

Amicable numbers are featured in the novel The Professor's Beloved Equation by Yoko Ogawa, and in the Japanese film based on it.

He discovered the theorem by which pairs of amicable numbers can be found; i.e., two numbers such that each is the sum of the proper divisors of the other.

The 9th Century Iraqi Muslim mathematician, physician, astronomer and translator Thābit ibn Qurra is credited as the first to study these numbers and their relation to amicable numbers.

The Thābit ibn Qurra theorem is a method for discovering amicable numbers invented in the ninth century by the Arab mathematician Thābit ibn Qurra.

Paul Auster's collection of short stories entitled True Tales of American Life contains a story ('Mathematical Aphrodisiac' by Alex Galt) in which amicable numbers play an important role.