On Some Magnified Fibonacci Numbers Modulo a Lucas Number
Ram Krishna Pandey
Department of Mathematics
Indian Institute of Technology Patna
Patliputra Colony, Patna - 800013
Let, as usual, Fn and Ln
denote the nth Fibonacci number and the nth
Lucas number, respectively. In this paper, we consider the Fibonacci
numbers F2, F3, ..., Ft.
Let n ≥ 1 be an integer such that 4n+2 ≤
t ≤ 4n+5 and m = F2n+2 +
F2n+4 = L2n+3.
We prove that
the integers F2 F2n+2, F3F2n+2, . . . , FtF2n+2 modulo m all belong to
the interval [F2n+1, 3F2n+2]. Furthermore, the endpoints of the
interval [F2n+1, 3F2n+2] are obtained only by the integers F4F2n+2 and
Full version: pdf,
(Concerned with sequence
Received September 28 2012;
revised version received January 21 2013.
Published in Journal of Integer Sequences, January 26 2013.
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