On a ternary Diophantine problem with mixed powers of primes
Alessandro Languasco ; Alessandro Zaccagnini
Acta Arithmetica, Tome 161 (2013), p. 345-362 / Harvested from The Polish Digital Mathematics Library
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Let 1 < k < 33/29. We prove that if λ₁, λ₂ and λ₃ are non-zero real numbers, not all of the same sign and such that λ₁/λ₂ is irrational, and ϖ is any real number, then for any ε > 0 the inequality |λ₁p₁+λ₂p²₂+λ₃p₃k+ϖ|≤(maxjpj)-(33-29k)/(72k)+ε has infinitely many solutions in prime variables p₁, p₂, p₃.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:279470 
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Alessandro Languasco; Alessandro Zaccagnini. On a ternary Diophantine problem with mixed powers of primes. Acta Arithmetica, Tome 161 (2013) pp. 345-362. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa159-4-4/