A non-integer property of elementary symmetric functions in reciprocals of generalised Fibonacci numbers

Nyblom, M 2003, 'A non-integer property of elementary symmetric functions in reciprocals of generalised Fibonacci numbers', The Fibonacci Quarterly, vol. 41, no. 2, pp. 152-155.


Document type: Journal Article
Collection: Journal Articles

Title A non-integer property of elementary symmetric functions in reciprocals of generalised Fibonacci numbers
Author(s) Nyblom, M
Year 2003
Journal name The Fibonacci Quarterly
Volume number 41
Issue number 2
Start page 152
End page 155
Total pages 4
Publisher Fibonacci Association
Abstract Define {Un} by U0=0, U_1=1 and Un=PUn-1-QUn-2 for n_>2, where P and Q are relatively prime positive integers. The author extended the classical result, viz. sum^n/r=1 1/r is not an integer for n>1, to sum^n/r=1 1/U_r with some conditions on P and Q in a previous paper and, developing it, establishes the following result in this paper: Suppose that {Un} is defined by a recurrence with P_>2 and Q<0. Let k < n and varphi(n,k) be the kth elementary symmetric function in 1/U1,1/U2,...,1/Un. Then, we can choose N, independent of P and Q, such that varphi(n,k) is not an integer for any n_>N and 1_
Copyright notice © Copyright American Mathematical Society 2004, 2010
ISSN 0015-0517
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