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Journal Articles European Journal of Combinatorics Year : 2018

On the degree of regularity of a certain quadratic Diophantine equation

S.D. Adhikari
  • Function : Author
L. Boza
  • Function : Author
M.P. Revuelta
  • Function : Author
M.I. Sanz
  • Function : Author

Abstract

We show that, for every positive integer r, there exists an integer b = b(r) such that the 4-variable quadratic Diophantine equation (x_1 − y_1)(x_2 − y_2) = b is r-regular. Our proof uses Szemerédi's theorem on arithmetic progressions.
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Dates and versions

hal-04147382 , version 1 (30-06-2023)

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S.D. Adhikari, L. Boza, Shalom Eliahou, M.P. Revuelta, M.I. Sanz. On the degree of regularity of a certain quadratic Diophantine equation. European Journal of Combinatorics, 2018, 70, pp.50-60. ⟨10.1016/j.ejc.2017.11.008⟩. ⟨hal-04147382⟩
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