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On the congruence $f(x)+g(y)+c\equiv 0\ ({\rm mod}\ xy)$, II (the quadratic case)

Volume 184 / 2018

A. Schinzel Acta Arithmetica 184 (2018), 1-6 MSC: 11D09, 11D25, 11D41. DOI: 10.4064/aa8449-7-2016 Published online: 22 January 2018

Abstract

The congruence given in the title is studied for $f(x) = ax^2 + a_1x \in \mathbb Z[x]$, $g(y) = by^2 + b_1y \in \mathbb Z[y]$, $c\in \mathbb Z\setminus \{0\}$ and with either $|ab|=1$, or $ab\ne 0$ and $\mathop{\rm Rad} c\mid(a_1,b_1a)$.

Authors

  • A. SchinzelInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
    e-mail

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