The integer part of a nonlinear form with integer variables

Abstract

Using the Davenport-Heilbronn method, we show that if λ 1 , λ 2 , . . . , λ 9 are positive real numbers, at least one of the ratios λ i

RETRACTED ARTICLE: Proofs to one inequality conjecture for the non-integer part of a nonlinear differential form

“…In this paper, we proved the conjecture for the non-integer part of a nonlinear differential form representing primes presented in [ 1 ] by using Tumura-Clunie type inequalities. Compared with the original proof, the new one is simpler and more easily understood.…”

“…Recently, Lai [ 1 ] proved that, for non-integer ( ), under certain conditions, there exist infinitely many primes such that And he also conjectured that the above results are true when primes in ( 1.1 ) are replaced by natural numbers . In this paper we shall give an affirmative answer to this conjecture.…”

“…Appl. 2015:Article ID 357, 2015 ) by using Tumura-Clunie type inequalities. Compared with the original proof, the new one is simpler and more easily understood.…”

Retraction Note: Proofs to one inequality conjecture for the non-integer part of a nonlinear differential form

“…The Editors-in-Chief have retracted this article because it shows significant overlap with an article by different authors that was simultaneously under consideration [1] and a previously published article [2]. Additionally, the article shows evidence of peer review manipulation.…”