If
is a prime , then the numerator of the
harmonic number
|
(1)
|
is divisible by
and the numerator of the generalized harmonic
number
|
(2)
|
is divisible by .
The numerators of
are sometimes known as Wolstenholme numbers.
These imply that if is prime, then
|
(3)
|
See also
Harmonic Number,
Wolstenholme
Number,
Wolstenholme Prime
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References
Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 85,
1994.Ribenboim, P. The
New Book of Prime Number Records. New York: Springer-Verlag, p. 21,
1989.Referenced on Wolfram|Alpha
Wolstenholme's Theorem
Cite this as:
Weisstein, Eric W. "Wolstenholme's Theorem."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WolstenholmesTheorem.html
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