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 not Necessary condition for amicability.

**References**

Dickson, L. E. *History of the Theory of Numbers, Vol. 1: Divisibility and Primality.* New York: Chelsea, 1952.

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1999-05-25