Autors: Dimitrov, S. I.
Title: On the number of pairs of positive integers x, y < H such that x^2+y^2+1, x^2+y^2+2 are square-free
Keywords: Square-free numbers, Asymptotic formula, Gauss sums

Abstract: In the present paper we show that there exist infinitely many consecutive square-free numbers of the form x^2+y^2+1, x^2+y^2+2. We also establish an asymptotic formula for the number of pairs of positive integers x, y < H such that x^2+y^2+1, x^2+y^2+2 are square-free.

References

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    , vol. 194, issue 3, pp. 281– 294, 2020, Poland, Acta Arithmetica

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