Wilson quotient
The Wilson quotient Wn for a given positive integer n is the rational number Γ(n)+1n, where Γ(x) is Euler’s Gamma function (since we’re dealing with integer inputs here, in effect this is merely a quicker way to write (n-1)!).
From Wilson’s theorem it follows that the Wilson quotient is an integer only if n is not composite. When n is composite, the numerator of the Wilson quotient is (n-1)!+1 and the denominator is n. For example, if n=7 we have numerator 721 with denominator 7, and since these have 7 as their greatest common divisor, in lowest terms the Wilson quotient of 7 is 103 (with 1 as tacit numerator). But for n=8 we have
W8=50418. |
References
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1
R. Crandall & C. Pomerance, Prime Numbers
: A Computational Perspective. New York: Springer (2001): 29.
Title | Wilson quotient |
---|---|
Canonical name | WilsonQuotient |
Date of creation | 2013-03-22 17:57:47 |
Last modified on | 2013-03-22 17:57:47 |
Owner | PrimeFan (13766) |
Last modified by | PrimeFan (13766) |
Numerical id | 6 |
Author | PrimeFan (13766) |
Entry type | Definition |
Classification | msc 11A51 |
Classification | msc 11A41 |