2
$\begingroup$

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?

Improve this question
$\endgroup$
3
  • 2
    $\begingroup$ Did you try Dickson's "Theory of Numbers"? $\endgroup$
    – Péter Komjáth
    Apr 23, 2013 at 5:08
  • 3
    $\begingroup$ ...or Google: the first Google hit for glaisher wolstenholme is <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. $\endgroup$
    – Noam D. Elkies
    Apr 23, 2013 at 5:27
  • $\begingroup$ Thanks. I have added these references to the Wikipedia page. $\endgroup$
    – Z.H.
    Apr 23, 2013 at 9:09

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.