From the 1 of 9 linked papers with an AI index.
9 papers
Exact classification of elliptic curves with rank and trivial $\Sha[2]$
Arkabrata Ghosh, Paul M. Voutier
The paper determines exactly when the elliptic curves (with distinct odd prime parameters) have Mordell‑Weil rank zero and a trivial 2‑torsion part of the Tate–Sh…
Perfect powers in sequences of polygonal numbers
Andrzej DÄ browski, Salah Eddine Rihane, Gökhan Soydan +1
Let denote the -th -gonal number. Consider the Diophantine equation for integers and . All solutions to this equation are known f…
Sharp bounds on the number of squares in recurrence sequences and solutions of
Paul M Voutier
We obtain best possible results for the number of coprime positive integer solutions of the equation in the title when is a positive integer, , or , w…
On the Guy-Kelly Conjecture for the No-Three-In-Line Problem
Paul M Voutier
We provide details of the error Gabor Ellmann found in 2004 in a heuristic argument of Guy and Kelly on this problem. This led to a correction of their conjectured upper bound for…
Bounds on the number of squares in recurrence sequences: (I)
Paul M Voutier
We continue and generalise our earlier investigations of the number of squares in binary recurrence sequences. Here we consider sequences, $\left( y_{k} \right)_{k=-\infty}^{\infty…
Bounds on the number of squares in recurrence sequences
Paul M Voutier
We investigate the number of squares in a very broad family of binary recurrence sequences with . We show that there are at most two distinct squares in such sequences (th…