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- W132694310 abstract "c a n n e v e r be an integer for n > 1. More generally, Nagell [3] showed that X^r=i m+rd c a n n o t t> e an integer for any positive integers m, n and d. As an extension of these results the author, in a recent paper [4], constructed further examples of positive rational termed series having non-integer partial sums. These partial sums were of the form Y^-i !T> where {Un} are the sequence of generalised Fibonacci numbers generated, for n > 2, via the recurrence relation Un = PUn^ - QUn-2, (1) with Uo — 0, U = 1 and (P,Q) a relatively prime pair of integers satisfying P > Q > 0 or P z/z 0, Q 2 and Q < 0, there can in fact be at most finitely many n such that one or more of the elementary symmetric functions in ^ - , ^ - , . . . jj- is an integer. To establish this result we will require two preliminary Lemmas, the first of which is a refinement of Bertrand's postulate due to Ingham [2]." @default.
- W132694310 created "2016-06-24" @default.
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- W132694310 date "2003-01-01" @default.
- W132694310 modified "2023-09-23" @default.
- W132694310 title "A non-integer property of elementary symmetric functions in reciprocals of generalised Fibonacci numbers" @default.
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