Andrew Bremner

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20062026

most citedOn squares in Lucas sequences

1 citations · 1 across the 3 of their papers we have counts for

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math.NT2026

There are infinitely many Hilbert cubes of dimension 3 in the set of squares

Andrew Bremner, Christian Elsholtz, Maciej Ulas

For an integer tuple $(a_{0}, a_{1}, \dots, a_{d})$ with $a_{i} \neq = 0$ for $i = 1, \dots, d$ , we define the associated Hilbert cube by \[ H(a_0;a_1,\ldots,a_d) = \left\{ a_0+\sum_{i=1}^d \vareps…

math.NT2007

Lucas sequences whose nth term is a square or an almost square

A. Bremner N. Tzanakis

(Below, \Box means "perfect square") Let $P$ and $Q$ be non-zero integers. The Lucas sequence ${U_{n} (P, Q)}$ is defined by $U_{0} = 0$ , $U_{1} = 1$ , $U_{n} = P U_{n - 1} - Q U_{n - 2}$ , $(n \geq 2)$ …

math.NT2006★ 1 cited

On squares in Lucas sequences

A. Bremner, N. Tzanakis

Let P and Q be non-zero integers. The Lucas sequence U_n(P,Q) is defined by U_0=0, U_1=1, U_n= P*U_{n-1}-Q*U_{n-2} for n >1. The question of when U_n(P,Q) can be a perfect square h…