An improvement of a lemma from Gauss’s first proof of quadratic reciprocity

Volume 65 / 2017

A. Schinzel, M. Skałba Bulletin Polish Acad. Sci. Math. 65 (2017), 29-33 MSC: Primary 11A15, 11L40. DOI: 10.4064/ba8109-4-2017 Published online: 18 April 2017


An upper estimate is given for the least prime $q$ such that $(d/q)=1$ and $(p/q)=-1$, where $d\not =0$ is a given integer and $p$ is a given prime satisfying $p\equiv 1\ ({\rm mod}\ 8)$ and $(d/p)=1$.


  • A. SchinzelInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
  • M. SkałbaInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland

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