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ISSN : 1226-0657

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Vol.11 No.1
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Representing Natural Numbers as Unique Sums of Positive Integers

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2004, v.11 no.1, pp.63-72
Laohakosol, Vichian
Chalermchai, Jiraporn
Laohakosol,, V. , & Chalermchai,, J. (2004). Representing Natural Numbers as Unique Sums of Positive Integers. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 11(1), 63-72.
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Abstract

It is known that each natural number can be written uniquely as a sum of Fibonacci numbers with suitably increasing indices. In 1960, Daykin showed that the sequence of Fibonacci numbers is the only sequence with this property. Consider here the problem of representing each natural number uniquely as a sum of positive integers taken from certain sequence allowing a fixed number, <TEX>$\cal{l}\geq2$</TEX>, of repetitions. It is shown that the <TEX>$(\cal{l}+1)$</TEX>-adic expansion is the only such representation possible.

keywords
representations, property, <tex> $P_{l}$</tex>, property <tex> P$_{l}$</tex>

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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