The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)
- Volume 11 Issue 1
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- Pages.63-72
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- 2004
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- 1226-0657(pISSN)
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- 2287-6081(eISSN)
REPRESENTING NATURAL NUMBERS AS UNIQUE SUMS OF POSITIVE INTEGERS
- Laohakosol, Vichian (Department of Mathematics, Kasetsrt University) ;
- Chalermchai, Jiraporn (Kasetsart University)
- Published : 2004.02.01
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,