Representing Natural Numbers as Unique Sums of Positive Integers

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Department of Mathematics, Kasetsrt University)
Chalermchai, Jiraporn (Kasetsart University)

Laohakosol, Vichian, & Chalermchai, Jiraporn. (2004). REPRESENTING NATURAL NUMBERS AS UNIQUE SUMS OF POSITIVE INTEGERS. 한국수학교육학회지시리즈B:순수및응용수학, 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>

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Vol.11 No.1

REPRESENTING NATURAL NUMBERS AS UNIQUE SUMS OF POSITIVE INTEGERS

Representing Natural Numbers as Unique Sums of Positive Integers

Abstract

한국수학교육학회지시리즈B:순수및응용수학