P. Voutier

activity

20122026

most citedPrimitive divisors of Lucas and Lehmer sequences, II

11 citations · 11 across the 6 of their papers we have counts for

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9 papers · 1 filter

math.NT2026

Exact classification of elliptic curves $y^{2} = x^{3} - pq x$ with rank $0$ and trivial $\Sha[2]$

Arkabrata Ghosh, Paul M. Voutier

For the elliptic curves $E_{p, q} : y^{2} = x^{3} - pq x$ where $p$ and $q$ are distinct odd primes, we establish necessary and sufficient conditions under which rank$\,E_{p,q}(\mathbb{Q}…

math.NT2026

Perfect powers in sequences of polygonal numbers

Andrzej Dąbrowski, Salah Eddine Rihane, Gökhan Soydan +1

Let $P_{s} (n)$ denote the $n$ -th $s$ -gonal number. Consider the Diophantine equation $P_{s} (n) = t^{m}$ for integers $n, s, t$ and $m > 2$ . All solutions to this equation are known f…

math.NT2025

Bounds on the number of squares in recurrence sequences: arbitrary $b$ , III

Paul M Voutier

We generalise our earlier work on the number of squares in binary recurrence sequences, ${y_{k}}_{k \geq - \infty}$ . In the notation of our previous papers, here we c…

math.NT2025

Bounds on the number of squares in recurrence sequences: $y_{0} = b^{2}$ (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…

math.NT2024

$n$ -defective Lehmer pairs for small $n$ : Corrections and Clarifications

Paul M. Voutier

We provide some corrections and clarifications of statements in \cite{Ab} and \cite{BHV} regarding elements in Lehmer sequences that have no primitive divisors for small $n$ .

math.NT2024

A family of cyclic quartic monogenic polynomials

Paul M. Voutier

We produce an explicit family of totally real cyclic quartic polynomials that are monogenic in many cases and, if the $ab c$ conjecture holds, generate distinct monogenic quartic fi…

Exact classification of elliptic curves y2=x3−pqx with rank 0 and trivial $\Sha[2]$

Perfect powers in sequences of polygonal numbers

Bounds on the number of squares in recurrence sequences: arbitrary b, III

Bounds on the number of squares in recurrence sequences: y0​=b2 (I)

n-defective Lehmer pairs for small n: Corrections and Clarifications

A family of cyclic quartic monogenic polynomials

Exact classification of elliptic curves $y^{2} = x^{3} - pq x$ with rank $0$ and trivial $\Sha[2]$

Bounds on the number of squares in recurrence sequences: arbitrary $b$ , III

Bounds on the number of squares in recurrence sequences: $y_{0} = b^{2}$ (I)

$n$ -defective Lehmer pairs for small $n$ : Corrections and Clarifications