On a linear homogeneous congruence

Volume 106 / 2006

A. Schinzel, M. Zakarczemny Colloquium Mathematicum 106 (2006), 283-292 MSC: Primary 11D79. DOI: 10.4064/cm106-2-8


The number of solutions of the congruence $a_1x_1+\cdots+a_kx_k\equiv 0\pmod n $ in the box $0\le x_i\le b_i$ is estimated from below in the best possible way, provided for all $i,j$ either $(a_i,n)\,|\, (a_j,n)$ or $ (a_j,n)\,|\, (a_i,n)$ or $n\,|\, [a_i,a_j]$.


  • A. SchinzelInstitute of Mathematics
    Polish Academy of Sciences
    P.O. Box 21
    00-956 Warszawa, Poland
  • M. ZakarczemnyInstitute of Mathematics
    Jagiellonian University
    Reymonta 4
    30-059 Kraków, Poland

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