P. Moree

activity

19992026

most citedConvoluted convolved Fibonacci numbers

24 citations · 285 across the 74 of their papers we have counts for

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Showing 2015Show all

5 papers · 1 filter

math.NT2015★ 2 cited

Forbidden integer ratios of consecutive power sums

Ioulia N. Baoulina, Pieter Moree

Let $S_{k} (m) := 1^{k} + 2^{k} + \dots + (m - 1)^{k}$ denote a power sum. In 2011 Bernd Kellner formulated the conjecture that for $m \geq 4$ the ratio $S_{k} (m + 1) / S_{k} (m)$ of two consecutive power sums…

math.NT2015

Cyclotomic coefficients: gaps and jumps

Oana-Maria Camburu, Emil-Alexandru Ciolan, Florian Luca +2

We improve several recent results by Hong, Lee, Lee and Park (2012) on gaps and Bzdȩga (2014) on jumps amongst the coefficients of cyclotomic polynomials. Besides direct improvemen…

math.NT2015

Counting terms $U_{n}$ of third order linear recurrences with $U_{n} = u^{2} + n v^{2}$

Emil-Alexandru Ciolan, Florian Luca, Pieter Moree

Given a recurrent sequence $U := {U_{n}}_{n \geq 0}$ we consider the problem of counting $M_{U} (x)$ , the number of integers $n \leq x$ such that $U_{n} = u^{2} + n v^{2}$ for some in…

math.NT2015

Salajan's conjecture on discriminating terms in an exponential sequence

Pieter Moree, Ana Zumalacárregui

Given a sequence of distinct positive integers $v_{1}, v_{2}, \dots$ and any positive integer $n$ , the discriminator $D_{v} (n)$ is defined as the smallest positive integer $m$ such $v_1,\…

math.NT2015

Addendum to the paper: "Artin Prime Producing Quadratics" [Abh. Math. Sem. Univ. Hamburg 77 (2007), 109--127; MR2379332 (2008m:11194)] by P. Moree

Yves Gallot, Pieter Moree

Can one find an integer $g$ and a polynomial $f$ , such that $g$ is a primitive root for many consecutive (different) prime values assumed by $f$ ? Moree considered this problem in 2…

Forbidden integer ratios of consecutive power sums

Cyclotomic coefficients: gaps and jumps

Counting terms Un​ of third order linear recurrences with Un​=u2+nv2

Salajan's conjecture on discriminating terms in an exponential sequence

Addendum to the paper: "Artin Prime Producing Quadratics" [Abh. Math. Sem. Univ. Hamburg 77 (2007), 109--127; MR2379332 (2008m:11194)] by P. Moree

Counting terms $U_{n}$ of third order linear recurrences with $U_{n} = u^{2} + n v^{2}$