Perfect Powers from Products of Terms in Lucas Sequences
نویسندگان
چکیده
Suppose that {Un}n≥0 is a Lucas sequence, and suppose that l1, . . . , lt are primes. We show that the equation Un1 · · ·Unm = ±l x1 1 · · · l xt t y , p prime, m < p, has only finitely many solutions. Moreover, we explain a practical method of solving these equations. For example, if {Fn}n≥0 is the Fibonacci sequence, then we solve the equation Fn1 · · ·Fnm = 2 x1 · 32 · 53 · · · 541100y under the restrictions: p is prime and m < p.
منابع مشابه
Diophantine equations with products of consecutive terms in Lucas sequences II
Here, we continue our work from [7] and study an inhomogeneous variant of a Diophantine equation concerning powers in products of consecutive terms of Lucas sequences. AMS Subject Classification: 11L07, 11N37, 11N60
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