Seminar za teoriju brojeva i algebru

Lokacija: 
PMF Matematički odsjek
Vrijeme: 
Petak, 21 Travanj, 2017 - 12:15 to 13:00

U petak 21.4.2017. s početkom u 12:15 u predavaonici br. 104,
Florian Luca (Wits University, Johannesburg; Max Planck Institute, Bonn; University of Ostrava)
održat će predavanje pod naslovom

        "On Diophantine quadruples of Fibonacci numbers".

Abstract:
A Diophantine k-tuple is a set of k-positive integers {a_1,...,a_k} such that
a_ia_j+1 is a square for all 1 <= i < j <= k. Recently, He, Togbe and Ziegler
proved that k <= 4. If (F_n)_{n>=0} denotes the Fibonacci sequence given by
F_0=0, F_1=1 and F_{n+2}=F_{n+1}+F_n for all n >= 0, then
{F_{2n},F_{2n+2},F_{2n+4}} is a Diophantine triple for all n >= 1.
In my talk, I will show that there only finitely many Diophantine quadruples
consisting of Fibonacci numbers.
This is a joint work with Y. Fujita.

Napominjemo da se predavanje održava izvan standardnog termina Seminara.
Pozivaju se članovi Seminara i svi zainteresirani da prisustvuju predavanju.

                                        Voditelji seminara:
                                        Andrej Dujella
                                        Ivica Gusić

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