Regularity of certain diophantine equations View Full Text


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Article Info

DATE

2019-04

AUTHORS

Bidisha Roy, Subha Sarkar

ABSTRACT

In Ramsey theory, there is a vast literature on regularity questions of linear diophantine equations. Some problems in higher degree have been considered recently. Here, we show that, for every pair of positive integers r and n, there exists an integer B=B(r) such that the diophantine equation ∏m=1n∑i=1kmam,ixm,i-∑j=1lmbm,jym,j=Bwith ∑i=1kmam,i=∑j=1lmbm,j∀m=1,…,nis r-regular, where km, lm are also positive integers and am,i,bm,j are non-zero integers. More... »

PAGES

19

References to SciGraph publications

  • 2017. On a Conjecture of Fox and Kleitman on the Degree of Regularity of a Certain Linear Equation in COMBINATORIAL AND ADDITIVE NUMBER THEORY II
  • 1933-12. Studien zur Kombinatorik in MATHEMATISCHE ZEITSCHRIFT
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    http://scigraph.springernature.com/pub.10.1007/s12044-019-0463-2

    DOI

    http://dx.doi.org/10.1007/s12044-019-0463-2

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