A Diophantine problem with a prime and three squares of primes

Alessandro Languasco; Alessandro Zaccagnini

doi:10.1016/j.jnt.2012.06.01

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arXiv · 1206.0246

A Diophantine problem with a prime and three squares of primes

Alessandro Languasco·Alessandro Zaccagnini

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Abstract

We prove that if $λ_1$, $λ_2$, $λ_3$ and $λ_4$ are non-zero real numbers, not all of the same sign, $λ_1 / λ_2$ is irrational, and $\varpi$ is any real number then, for any $\eps > 0$ the inequality $ \bigl|λ_1 p_1 + λ_2 p_2^2 + λ_3 p_3^2 + λ_4 p_4^2 + \varpi \bigr| \le \bigl(\max_j p_j \bigr)^{-1 / 18 + \eps} $ has infinitely many solution in prime variables $p_1$, ..., $p_4$

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Alessandro Languasco, Alessandro Zaccagnini. 2012-06-01. A Diophantine problem with a prime and three squares of primes. https://doi.org/10.1016/j.jnt.2012.06.01

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