Thabit ibn Qurra's rule for amicable numbers
Regla de Thabit para los números amigos
- Date
- c. 870 · confidence medium
- Place
- Baghdad, Iraq
- Credited to
- Thabit ibn Qurra
- People
- 👤 Thábit ibn Qurra836–901
- Field
- Knowledge & symbols
What was discovered
First general formula for generating pairs of amicable numbers (each equal to the sum of the other's divisors) from certain primes. It is one of the first number-theory theorems since Euclid.
The pair 17296-18416 was found by Kamal al-Din al-Farisi around 1300, before Fermat (1636), and Muhammad Baqir Yazdi found the pair 9363584-9437056 in the 17th century, before Descartes.
What it led to
- amicable pairs found by al-Farisi (17296, 18416) and Yazdi
- formula generalised by Euler
- additive number theory