## View abstract

### Session S09 - Number Theory in the Americas

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

## Generalized Fibonacci and Pell numbers

### Jhon Bravo

#### U. Cauca, Colombia   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak6484a15ebeb39c3612c798e4351ee946').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy6484a15ebeb39c3612c798e4351ee946 = 'jbr&#97;v&#111;' + '&#64;'; addy6484a15ebeb39c3612c798e4351ee946 = addy6484a15ebeb39c3612c798e4351ee946 + '&#117;n&#105;c&#97;&#117;c&#97;' + '&#46;' + '&#101;d&#117;' + '&#46;' + 'c&#111;'; var addy_text6484a15ebeb39c3612c798e4351ee946 = 'jbr&#97;v&#111;' + '&#64;' + '&#117;n&#105;c&#97;&#117;c&#97;' + '&#46;' + '&#101;d&#117;' + '&#46;' + 'c&#111;';document.getElementById('cloak6484a15ebeb39c3612c798e4351ee946').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy6484a15ebeb39c3612c798e4351ee946 + '\'>'+addy_text6484a15ebeb39c3612c798e4351ee946+'<\/a>';

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.

Joint work with J. L. Herrera (U. Cauca, Colombia) and F. Luca (Wits, South Africa and UNAM, Mexico).