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Perfect Fibonacci and Lucas numbers. (English) Zbl 0972.11007

Using elementary means, the author shows that no Fibonacci or Lucas number is perfect.

MSC:

11A25 Arithmetic functions; related numbers; inversion formulas
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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References:

[1] Cohn J.H.E.,Square Fibonacci numbers, etc., Fibo. Quart.,2 (1964). · Zbl 0126.07201
[2] Dickson, L. E., History of the Theory of Numbers, Vol. I (1966), New York: Divisiblity and Primality, Chelsea Publishing Company, New York · Zbl 0958.11500
[3] Luca, F., Euler Indicators of Lucas Sequences, Bull. Math. Soc. Sc. Mat. Roumanie, Tome, 40, 88, 151-163 (1997) · Zbl 0922.11003
[4] Luca, F., Arithmetic functions of Fibonacci and Lucas numbers, Fibo. Quart., 37, 265-268 (1999) · Zbl 0936.11007
[5] Ribenboim, P., Square Classes of Fibonacci and Lucas numbers, Portugaliae Math., 46, 1, 159-176 (1989) · Zbl 0687.10005
[6] Robbins, N., On Fibonacci numbers of the form px^2where p is a prime, Fibo, Quart., 21, 266-271 (1983) · Zbl 0523.10003
[7] Rosen K.H.,Elementary number theory and its applications, Addison-Wesley, 1984. · Zbl 0546.10001
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