Journal of Integer Sequences, Vol. 16 (2013), Article 13.1.7

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 F4n+2F2n+2, respectively.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequence A000045.)

Received September 28 2012; revised version received January 21 2013. Published in Journal of Integer Sequences, January 26 2013.

Return to Journal of Integer Sequences home page