On the number of pairs of positive integers x, y ≤ H such that x²+y²+1, x²+y²+2 are square-free

2019/01/05 by Dimitrov, S. I.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1901.04838

Abstract

In the present paper we show that there exist infinitely many consecutive square-free numbers of the form x²+y²+1, x²+y²+2. We also give an asymptotic formula for the number of pairs of positive integers x, y ≤ H such that x²+y²+1, x²+y²+2 are square-free.

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