A Diophantine problem with prime variables

Abstract

We study the distribution of the values of the form ${\lambda }_1{p}_1+{\lambda }_2{p}_2+{\lambda }_3{p}_3^k$, where ${\lambda }_1$, ${\lambda }_2$ and ${\lambda }_3$ are non-zero real number not all of the same sign, with ${\lambda }_1/{\lambda }_2$ irrational, and $p_1$, $p_2$ and $p_3$ are prime numbers. We prove that, when $1<k<4/3$, these value approximate rather closely any prescribed real number.

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Cited by in corpus (2)

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