Euler's Rule
The numbers 
and 
are Amicable Numbers if the three Integers
 |  |  | |
 | | | |
 | |  |
are all Prime numbers for some Positive Integer
satisfying 
(Dickson 1952, p. 42). However, there are exotic Amicable Numbers which do not satisfy Euler's rule, so it is a Sufficient but notNecessary condition for amicability.See also Amicable Numbers
References
Dickson, L. E. History of the Theory of Numbers, Vol. 1: Divisibility and Primality. New York: Chelsea, 1952.
- Otter's Tree Enumeration Constants
- Outdegree
- Outer Automorphism Group
- Outer Product
- Oval
- Oval of Descartes
- Ovals of Cassini
- Overlapping Resonance Method
- Oversampling
- Ovoid
- Paasche's Index
- Packing
- Packing Density
- p-adic Number
- Padovan Sequence
- Padé Approximant
- Padé Conjecture
- Painlevé Property
- Painlevé Transcendents
- Pair
- Paired t-Test
- Pair Sum
- Paley Class
- Paley Construction
- Paley's Theorem