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Session S09 - Number Theory in the Americas

Thursday, July 22, 19:00 ~ 19:30 UTC-3

Generalized Fibonacci and Pell numbers

Jhon Bravo

The Pell sequence $(P_n)_{n\geq 0}$ is the second order linear recurrence defined by $P_n=2P_{n-1}+P_{n-2}$ with initial conditions $P_0=0$ and $P_1=1$. In this talk, we present some recent work on a generalization of the Pell sequence called the $k$-Pell sequence $(P_n^{(k)})_{n}$ which is generated by a recurrence relation of a higher order. We report about some arithmetic properties of $(P_n^{(k)})_{n}$ and study some Diophantine equations involving Fibonacci and $k$-Pell numbers.