On arithmetic progressions in Lucas sequences – II
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DOI: 10.1016/j.jnt.2019.02.015
Abstract: Abstract In this paper, we provide an effective and practical method to find all three term arithmetic progressions in a given Lucas sequence of the first or second kind. Our interest is the case when… read more here.
Keywords: progressions lucas; lucas sequences; arithmetic progressions;
On Diophantine equations involving Lucas sequences
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DOI: 10.1515/math-2019-0073
Abstract: Abstract In this paper, we shall study the Diophantine equation un = R(m)P(m)Q(m), where un is a Lucas sequence and R, P and Q are polynomials (under weak assumptions). read more here.
Keywords: involving lucas; lucas sequences; lucas; diophantine equations ... See more keywords
A New Approach to k-Oresme and k-Oresme-Lucas Sequences
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DOI: 10.3390/sym16111407
Abstract: In this study, the k-Oresme and k-Oresme-Lucas sequences are defined, and some terms of these sequence are given. Then, the relations between the terms of the k-Oresme and k-Oresme-Lucas sequences are presented. In addition, we… read more here.
Keywords: new approach; oresme lucas; lucas sequences; oresme oresme ... See more keywords
Combinatorial Analysis of k-Oresme and k-Oresme-Lucas Sequences
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DOI: 10.3390/sym17050697
Abstract: In this study, firstly the definitions and basic algebraic properties of k-Oresme and k-Oresme–Lucas sequences are given. Then, various summation formulae are derived with the help of the first and second derivatives of two polynomials… read more here.
Keywords: analysis; oresme lucas; lucas sequences; oresme oresme ... See more keywords
Terms of Lucas sequences having a large smooth divisor
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DOI: 10.4153/s0008439522000248
Abstract: Abstract We show that the $Kn$ –smooth part of $a^n-1$ for an integer $a>1$ is $a^{o(n)}$ for most positive integers n. read more here.
Keywords: smooth divisor; large smooth; terms lucas; lucas sequences ... See more keywords