A Wolstenholme number is a
number
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers c ...
that is the
numerator
A fraction (from la, fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight ...
of the
generalized harmonic number
In mathematics, the -th harmonic number is the sum of the reciprocals of the first natural numbers:
H_n= 1+\frac+\frac+\cdots+\frac =\sum_^n \frac.
Starting from , the sequence of harmonic numbers begins:
1, \frac, \frac, \frac, \frac, \dot ...
''H''
''n'',2.
The first such numbers are 1, 5, 49, 205, 5269, 5369, 266681, 1077749, ... .
These numbers are named after
Joseph Wolstenholme
Joseph Wolstenholme (30 September 1829 – 18 November 1891) was an English mathematician.
Wolstenholme was born in Eccles near Salford, Lancashire, England, the son of a Methodist minister, Joseph Wolstenholme, and his wife, Elizabeth, ''née' ...
, who proved
Wolstenholme's theorem In mathematics, Wolstenholme's theorem states that for a prime number p \geq 5, the congruence
: \equiv 1 \pmod
holds, where the parentheses denote a binomial coefficient. For example, with ''p'' = 7, this says that 1716 is one more than a multiple ...
on modular relations of the generalized harmonic numbers.
References
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Integer sequences
{{Num-stub