On perfect powers that are sums of two Pell numbers

Hyacinthe Aboudja,Mohand Hernane,Salah Eddine Rihane,Alain Togbé

PERIODICA MATHEMATICA HUNGARICA（2020）

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摘要

Let P_k denote the k th term of the Pell sequence. In this paper we find all solutions of the exponential Diophantine equation P_n+P_m = y^s in positive integer variables ( m , n , y , s ) under the assumption n ≡ m 2 .

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关键词

Perfect numbers, Exponential equations, Perfect powers, p-adic valuation

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