Wolstenholme's Conjecture
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Conjecture
Let $n \in \Z_{>0}$ be a (strictly) positive integer.
Suppose that:
- $\dbinom {2 n - 1} {n - 1} \equiv 1 \pmod {n^3}$
where $\dbinom {2 n - 1} {n - 1}$ denotes a binomial coefficient.
Then $n$ is a prime number
Also see
- Wolstenholme's Theorem, of which this is the converse
Source of Name
This entry was named for Joseph Wolstenholme.
Sources
- 1862: Joseph Wolstenholme: On certain properties of prime numbers (Quart. J. Pure Appl. Math. Vol. 5: pp. 35 – 39)