On the degree of regularity of a certain quadratic Diophantine equation
Résumé
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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