16 citations · 43 across the 47 of their papers we have counts for
49 papers
A Quixotic Proof of Fermat's Two Squares Theorem for Prime Numbers
Roland Bacher
Every odd prime number p can be written in exactly (p + 1)/2 ways as a sum ab+cd of two ordered products ab and cd such that min(a, b) > max(c, d). An easy corollary is a proof of…
Euclid meets Popeye: The Euclidean Algorithm for matrices
Roland Bacher
An analogue of the Euclidean algorithm for square matrices of size 2 with integral non-negative entries and strictly positive determinant defines a finite set …
Yet another Proof of an old Hat
Roland Bacher
Every odd prime number p can be written in exactly (p + 1)/2 ways as a sum ab + cd with min(a, b) > max(c, d) of two ordered products. This gives a new proof Fermat's Theorem expre…
Generic numerical semigroups
Roland Bacher
The use of compositions simplifies some aspects of the theory of numerical semigroups. We illustrate this by giving a new proof for the asymptotic number C((1 + $\sqrt$ 5)/2) g of…
Weyl-Mahonian Statistics for Weighted Flags of Type A-D
Roland Bacher
We relate properties of weighted flags (or multiflags) of type AD to statistics of the corresponding Weyl groups. For type A, we recover the Mahonian statistics on symmetric groups…
On the number of perfect lattices
Roland Bacher
We show that the number of non-similar perfect -dimensional lattices satisfies eventually the inequalities for arbitrary smallstrictly posit…