Séminaire Combinatoire et Théorie des Nombres ICJ

Congruences for coefficients of rational functions

par Frits Beukers (Universiteit Utrecht)

Bât. Braconnier, salle Fokko du Cloux (ICJ, Université Lyon 1)

Bât. Braconnier, salle Fokko du Cloux

ICJ, Université Lyon 1

We discuss generalizations of the well-known congruences u(mp^r) = u(mp^(r-1)) mod p^r of the Lucas sequence u(0)=2, u(1)=1, u(2)=3, u(3)=4, ... Here m,r are arbitrary positive integers and p is an arbitrary prime. The generating function of the u(n) is (x+2x^2)/(1-x-x^2). It turns out that similar congruences occur for coefficients of certain multivariable rational functions. We explore this phenomenon. The ultimate goal will be to find cases where congruences mod p^(2r) and p^(3r) hold.
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