A Quadratic Diophantine Equation Involving Generalized Fibonacci Numbers by Ana Paula Chaves, Pavel Trojovský

“…In this paper, we shall solve the Diophantine equation <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>F</mi> <mi>n</mi> <mrow> <mo stretchy="false">(</mo> <mi>k</mi> <mo stretchy="false">)</mo> </mrow> </msubsup> <mo>=</mo> <msup> <mrow> <mo stretchy="false">(</mo> <msubsup> <mi>F</mi> <mi>m</mi> <mrow> <mo stretchy="false">(</mo> <mi>l</mi> <mo stretchy="false">)</mo> </mrow> </msubsup> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula>, in positive integers <inline-formula> <math display="inline"> <semantics> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> <mo>,</mo> <mi>k</mi> </mrow> </semantics> </math> </inline-formula> and <i>l</i>.…”
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On Repdigits as Sums of Fibonacci and Tribonacci Numbers by Pavel Trojovský

Subjects: “…Diophantine equations…”
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On Fibonacci Numbers of Order <i>r</i> Which Are Expressible as Sum of Consecutive Factorial Numbers by Eva Trojovská , Pavel Trojovský

Subjects: “…diophantine equation…”
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Some Diophantine Problems Related to <i>k</i>-Fibonacci Numbers by Pavel Trojovský, Štěpán Hubálovský

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Repdigits as Product of Terms of <i>k</i>-Bonacci Sequences by Petr Coufal, Pavel Trojovský

“…Our main tools are the transcendental method (for Diophantine equations) together with the theory of continued fractions (reduction method).…”
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