On the Diophantine equation σ₂(X_n)=σ_n(X_n)

2022/03/08 by Miska, Piotr, Ulas, Maciej
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2203.03942

Abstract

In this note we investigate the set S(n) of positive integer solutions of the title Diophantine equation. In particular, for a given n we prove boundedness of the number of solutions, give precise upper bound on the common value of σ₂(X_n) and σ_n(X_n) together with the biggest value of the variable x_n appearing in the solution. Moreover, we enumerate all solutions for n≤ 16 and discuss the set of values of x_n/x_n-1 over elements of S(n).

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