NEW ZEALAND JOURNAL OF MATHEMATICS Volume 40 (2010), 1-13
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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