Resources on Wolstenholme's theorem

Asked Apr 23 '13 at 04:54

Active Apr 23 '13 at 04:54

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In Wikipedia entry on Wolstenholme's theorem, it says

The second formulation $\binom{ap}{bp}=\binom{a}{b}\pmod{p^3}$ of Wolstenholme's theorem is due to J. W. L. Glaisher.

But there is no reference to it. Does anyone know which paper of J. W. L. Glaisher contains the above statement?

asked Apr 23 '13 at 04:54

Z.H.

2

Did you try Dickson's "Theory of Numbers"? – Péter Komjáth Apr 23 '13 at 05:08
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...or Google: the first Google hit for glaisher wolstenholme is http://arxiv.org/pdf/1111.3057.pdf, where on page 25 there are three references ([32] to [34]) to papers by Glaisher published in the Q.J.Math. in 1900 or 1901; the second of these ("On the residues of the sums of products of the first $p - 1$ numbers, and their powers, to modulus $p^2$ or $p^3$") seems particularly promising. – Noam D. Elkies Apr 23 '13 at 05:27
Thanks. I have added these references to the Wikipedia page. – Z.H. Apr 23 '13 at 09:09

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