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It is shown that period, rank and order of the ) , ( b a -Fibonacci sequence remain invariant by extension to the generalized ) , , , ( d c b a -Lucas sequence provided a specific determinant is relatively prime to the modulus. Given an odd prime modulus p and the 1  p exceptional ) , ( b a -Lucas sequences, for which p divides the discriminant of these sequences, we determine the corresponding periods and relate them to those of the ) , ( b a -Fibonacci sequence. The results can be viewed as extended versions of classical results by Wall in case ) 1 , 1 ( ) , (  b a . 2010 Mathematics Subject Classification : 11B39, 11B50.

From the Modular Properties of (a,b)-Fibonacci Sequences to those of Generalized Lucas Sequences