Florian Luca Instituto de Matemáticas
نویسندگان
چکیده
Let σk(n) be the sum of the kth powers of the divisors of n. Here, we prove that if (Fn)n≥1 is the Fibonacci sequence, then the only solutions of the equation σk(Fm) = Fn in positive integers k ≥ 2, m and n have k = 2 and m ∈ {1, 2, 3}. The proof uses linear forms in two and three logarithms, lattice basis reduction, and some elementary considerations.
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This paper bij Florian Luca and Herman te Riele is an extended version of the 10th biennial Beeger Lecture, presented by Florian Luca on April 23, 2010 during the Nederlands Mathematisch Congres in Utrecht. Florian Luca (born 1969 in Romania) is full professor at the Instituto de Matemáticas, UNAM, Morelia, México. His research interests are abstract algebra, algebraic number theory, and Diopha...
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