On the problem of Pillai with Padovan numbers and powers of 3

What is it about?

Let $ \{P_{n}\}_{n\geq 0} $ be the sequence of Padovan numbers defined by $ P_0=0 $, $ P_1 =1, ~P_2=1$, and $ P_{n+3}= P_{n+1} +P_n$ for all $ n\geq 0 $. In this paper, we find all integers $ c $ admitting at least two representations as a difference between a Padovan number and a power of $ 3 $.

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Photo by Stefano Segato on Unsplash

Photo by Stefano Segato on Unsplash

Why is it important?

Applies Baker's methods

Perspectives