Math and Stat Colloquium

• April 18, 2024
• 4:00 PM - 5:00 CST
• IES 110
• Open to the public.
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• Details

  Speaker: Rigoberto Florez
  https://www.rigoflorez.com/
  Title. The strong divisibility property and the resultant of generalized Fibonacci polynomials
  Abstract. A second order polynomial sequence is of Fibonacci-type (Lucas-type) if its Binet formula has a structure similar to that for Fibonacci (Lucas) numbers. Those are known as generalized Fibonacci polynomials GFP. Some known examples are: Fibobacci Polynomials, Pell polynomials, Fermat polynomials, Chebyshev polynomials, Morgan-Voyce polynomials, Lucas polynomials, Pell-Lucas polynomials, Fermat-Lucas polynomials, Chebyshev polynomials, Vieta and Vieta-Lucas polynomials.
  It is known that the greatest common divisor of two Fibonacci numbers is again a Fibonacci number. It is called the strong divisibility property. However, this property does not hold for every second order recursive sequence. We give a characterization of GFPs that satisfy the strong divisibility property. We also give formulas to evaluate the gcd of GFPs that do not satisfy the strong divisibility property.
  In the end of the talk we talk about the irreducibility of GFP.
  Joint work with M. Diaz-Noguera, R. Higuita, M. Romero-Rojas, R. Ramirez, and J.C.
  Saunders.