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Diophantine inequalities involving a prime and an almost-prime

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Abstract We prove that there are infinitely many solutions of | λ 0 + λ 1 p + λ 2 P 3 | p − 1 131 , where λ… Click to show full abstract

Abstract We prove that there are infinitely many solutions of | λ 0 + λ 1 p + λ 2 P 3 | p − 1 131 , where λ 0 is an arbitrary real number and λ 1 , λ 2 ∈ R with λ 2 ≠ 0 and 0 > λ 1 λ 2 not in Q . This improves a result by Harman.

Keywords: diophantine inequalities; inequalities involving; involving prime; prime almost; almost prime

Journal Title: Journal of Number Theory
Year Published: 2017

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