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Published in 2019 at "Journal of Number Theory"
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…
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Keywords:
progressions lucas;
lucas sequences;
arithmetic progressions;
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Published in 2019 at "Open Mathematics"
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).
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Keywords:
involving lucas;
lucas sequences;
lucas;
diophantine equations ... See more keywords
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2
Published in 2022 at "Canadian Mathematical Bulletin"
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.
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Keywords:
smooth divisor;
large smooth;
terms lucas;
lucas sequences ... See more keywords