18 research outputs found
On the Problem of Pillai with Fibonacci numbers and powers of
International audienceConsider the sequence {Fn} nβ₯0 of Fibonacci numbers defined by F 0 = 0, F 1 = 1 and F n+2 = F n+1 + Fn for all n β₯ 0. In this paper, we find all integers c having at least two representations as a difference between a Fibonacci number and a power of 3
Repdigits as sums of three Padovan numbers
International audienceLet be the sequence of Padovan numbers defined by , , and for all . In this paper, we find all repdigits in base which can be written as a sum of three Padovan numbers
On the --coordinates of Pell equations that are products of two Padovan numbers
Let be the sequence of Padovan numbers defined by , , and for all . In this paper, we find all positive square-free integers such that the Pell equations , where , have at least two positive integer solutions and such that each of and is a product of two Padovan numbers