11 citations · 23 across the 23 of their papers we have counts for
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Lattice Equable Quadrilaterals I -- Parallelograms
Christian Aebi, Grant Cairns
This paper studies equable parallelograms whose vertices lie on the integer lattice. Using Rosenberger's Theorem on generalised Markov equations, we show that the g.c.d. of the sid…
The Quartic Residues Latin Square
Christian Aebi, Grant Cairns
We establish an elementary, but rather striking pattern concerning the quartic residues of primes that are congruent to 5 modulo 8. Let be a generator of the multiplicative…
Sums of Quadratic residues and nonresidues
Christian Aebi, Grant Cairns
It is well known that when a prime is congruent to 1 modulo 4, the sum of the quadratic residues equals the sum of the quadratic nonresidues. In this note we give analogous res…
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.
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…
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.