On additive representation function of general sequences |
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| Authors: | G. Horváth |
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| Affiliation: | (1) Institute of Mathematics, Department of Mathematical Analysis, College of Dunaújváros, Táncsics M. u. 1/A., H-2401 Dunaújváros, Hungary |
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| Abstract: | Let 0 ≦ a 1 < a 2 < ? be an infinite sequence of integers and let r 1(A, n) = |(i;j): a i + a j = n, i ≦ j|. We show that if d > 0 is an integer, then there does not exist n 0 such that d ≦ r 1 (A, n) ≦ d + [√2d + ½] for n > n 0. |
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| Keywords: | additive number theory general sequences additive representation function |
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