P. Voutier

activity

20082026

most citedAn effective lower bound for the height of algebraic numbers

120 citations · 320 across the 32 of their papers we have counts for

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5 papers · 1 filter

math.NT2026

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

Paul M Voutier

For binary recurrence sequences, $(y_{k})_{k \in Z}$ , arising from the solutions of generalised Pell equations, $X^{2} - d Y^{2} = c$ , where $y_{0}$ is any positive squa…

math.NT2026

Smyth's Conjecture on the Mahler Measure of non-reciprocal trinomials of height $1$

Paul M Voutier

We prove a conjecture of Smyth on the Mahler measure of non-reciprocal trinomials of height $1$ , determining exactly when their Mahler measures are greater than or less than $M(x+y…

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.CO2026

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: y0​=b2 (II)

Smyth's Conjecture on the Mahler Measure of non-reciprocal trinomials of height 1

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

Perfect powers in sequences of polygonal numbers

On the Guy-Kelly Conjecture for the No-Three-In-Line Problem

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

Smyth's Conjecture on the Mahler Measure of non-reciprocal trinomials of height $1$

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