16 citations · 43 across the 47 of their papers we have counts for
13 papers · 1 filter
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 …
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…
The Stern Sequence and Moments of Minkowski's Question Mark Function
Roland Bacher
1 : We use properties of the Stern Sequence for numerical computations of moments associated to Minkowski's Question Mark function.
On geodesics of phyllotaxis
Roland Bacher
Seeds of sunflowers are often modelled by the map leading to a roughly uniform repartition with two consecutive seeds separated by the diver…
Universal convex coverings
Roland Bacher
In every dimension , we establish the existence of a constant and of a subset of such that the following holds: $\mathcal C+\mathcal U_d…