On some polynomial values of repdigit numbers

Abstract

We study the equal values of repdigit numbers and the k dimensional polygonal numbers. We state some effective finiteness theorems, and for small parameter values we completely solve the corresponding equations.

On some polynomial values of repdigit numbers

“…This concept is needed because of the huge number of trivial solutions; on the other hand, such solutions of (3) can be listed easily for any fixed k. Remarks. In the original paper [19] all the solutions are determined. We considered some other related equations, corresponding to larger values of the parameter k of the polynomial f k,m (x), that lead to genus 2 equations.…”

“…We state some effective finiteness theorems, and for small parameter values we completely solve the corresponding equations. The full paper based on the results mentioned below will be published in Periodica Mathematica Hungarica [19].…”

Finiteness results for Diophantine triples with repdigit values

“…Questions concerning Diophantine equations involving repdigits have been considered by Keith [11], Marques and Togbé [17] and Kovács et.al. [12], to name just a few. In this paper, we combine the Diophantine tuples with repdigits and thus consider Diophantine triples having products increased by 1 in the set of repdigits in the fixed base g.…”