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math.NT2015
Wolstenholme again
Christian Aebi, Grant Cairns
We give an elementary and self-contained proof of the equivalence of a collection of Wolstenholme-type congruences due to Helou and Terjanian.
math.NT2013
Morley's other miracle: $\displaystyle 4^{p-1}\equiv\pm (\smallmatrix p-1 \frac{p-1}{2} \endsmallmatrix) \pmod {p^3} $
Christian Aebi, Grant Cairns
Frank Morley is famous for his theorem concerning the angle trisectors of a triangle. This note gives an elementary proof of another result of Morley's, which relates the middle bi…
math.NT2013
Wilson Theorems for Double-, Hyper-, Sub- and Super-factorials
Christian Aebi, Grant Cairns
We present generalisations of Wilson's theorem for double factorials, hyperfactorials, subfactorials and superfactorials.