On the Diophantine equations $$\varvec{P_{n}=b^{d}Q_{m}+Q_{k}}$$ and $$\varvec{Q_{n}=b^{d}P_{m}+P_{k}}$$ involving Pell and Pell–Lucas numbers

Adédji, Kouèssi Norbert; Faye, Mariama Ndao; Togbé, Alain

doi:10.1007/s12044-024-00784-4

Proc Math Sci

2024

DOI: 10.1007/s12044-024-00784-4

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On the Diophantine equations $$\varvec{P_{n}=b^{d}Q_{m}+Q_{k}}$$ and $$\varvec{Q_{n}=b^{d}P_{m}+P_{k}}$$ involving Pell and Pell–Lucas numbers

Kouèssi Norbert Adédji,

Mariama Ndao Faye,

Alain Togbé

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2024

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Cited by 2 publications

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On b-concatenations of Padovan and Perrin numbers

Adédji,

Kandhil,

Togbé

2024

Bol. Soc. Mat. Mex.

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On b-concatenations of Padovan and Perrin numbers

Adédji,

Kandhil,

Togbé

2024

Bol. Soc. Mat. Mex.

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On Mixed 𝐵-Concatenations of Pell and Pell–Lucas Numbers which are Pell Numbers

Adédji,

Trebješanin

2024

MathPann

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Let (𝑃𝑛)𝑛≥0 and (𝑄𝑛)𝑛≥0 be the Pell and Pell–Lucas sequences. Let 𝑏 be a positive integer such that 𝑏 ≥ 2. In this paper, we prove that the following two Diophantine equations 𝑃𝑛 = 𝑏𝑑𝑃𝑚 + 𝑄𝑘 and 𝑃𝑛 = 𝑏𝑑𝑄𝑚 + 𝑃𝑘 with 𝑑, the number of digits of 𝑃𝑘 or 𝑄𝑘 in base 𝑏, have only finitely many solutions in nonnegative integers (𝑚, 𝑛, 𝑘, 𝑏, 𝑑). Also, we explicitly determine these solutions in cases 2 ≤ 𝑏 ≤ 10.

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On the Diophantine equations $$\varvec{P_{n}=b^{d}Q_{m}+Q_{k}}$$ and $$\varvec{Q_{n}=b^{d}P_{m}+P_{k}}$$ involving Pell and Pell–Lucas numbers

Cited by 2 publications

References 11 publications

On b-concatenations of Padovan and Perrin numbers

On b-concatenations of Padovan and Perrin numbers

On Mixed 𝐵-Concatenations of Pell and Pell–Lucas Numbers which are Pell Numbers

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