A DIOPHANTINE EQUATION INVOLVING C-NOMIAL COEFFICIENTS

Diego Marques, Alain Togbe

Abstract


Let C_n be the n-th Fibonacci number (C_n=F_n) or the n-th Lucas
number (C_n=L_n). For 1?k?m,let
...
be the corresponding C-nomial coefficient. In this paper, we prove that
the only solutions of the Diophantine equation
...
in positive integers m, k, a, b with a>1, are (m, k, a, b)=(1,1,a,b), (5,1,1,b),
(12,1,2,b), and (5,3,1,1), for C_n=F_n and (m, k, a, b)=(1,1,a,b) in
the case C_n=L_n.

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