On the k-free values of the polynomial xyk+ C

K. Lapkova*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Consider the polynomial f(x, y) = xyk+ C for k≥ 2 and any nonzero integer constant C. We derive an asymptotic formula for the k-free values of f(x, y) when x, y≤ H. We also prove a similar result for the k-free values of f(p, q) when p, q≤ H are primes, thus extending Erdős’ conjecture for our specific polynomial. The strongest tool we use is a recent generalization of the determinant method due to Reuss.

Original languageEnglish
Pages (from-to)190-207
Number of pages18
JournalActa Mathematica Hungarica
Issue number1
Publication statusPublished - 2016
Externally publishedYes


  • primary 11N32
  • secondary 11N37

ASJC Scopus subject areas

  • Mathematics(all)

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