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Pré-Publication, Document De Travail Année : 2023

Square-free pairs n^2 + n + 1, n ^2 + n + 2

Stoyan Dimitrov
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Résumé

In this paper we prove that there exist infinitely many square-free pairs of the form n^2+n+1, n^2+n+2. We also establish an asymptotic formula for the number of such square-free pairs when n does not exceed given sufficiently large positive number. A key point in our proof is the application of bijective correspondence between the number of representations of number by binary quadratic form and the incongruent solutions of quadratic congruence.
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Dates et versions

hal-03735444 , version 1 (21-07-2022)
hal-03735444 , version 2 (09-06-2023)

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  • HAL Id : hal-03735444 , version 2

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Stoyan Dimitrov. Square-free pairs n^2 + n + 1, n ^2 + n + 2. 2023. ⟨hal-03735444v2⟩
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