Let λ1,λ2,λ3,λ4 be non-zero real numbers, not all of the same sign, w real. Suppose that the ratios λ1/λ2,λ1/λ3 are irrational and algebraic. Then there are infinitely many solutions in primes pj, j = 1, 2,3,4...Let λ1,λ2,λ3,λ4 be non-zero real numbers, not all of the same sign, w real. Suppose that the ratios λ1/λ2,λ1/λ3 are irrational and algebraic. Then there are infinitely many solutions in primes pj, j = 1, 2,3,4, to the inequality |λ1p1 +λ2p^2/2 +λ3p^2/3+|λ4p^2/4+■(max{p1,p^2/2,p^2/3,p^2/4})-^5/64. This improves the earlier result.展开更多
基金The authors thank the referees for their time and comments. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11871193, 11471112)the Key Research Project of Henan Province Higher Education (No. 17A110009).
文摘Let λ1,λ2,λ3,λ4 be non-zero real numbers, not all of the same sign, w real. Suppose that the ratios λ1/λ2,λ1/λ3 are irrational and algebraic. Then there are infinitely many solutions in primes pj, j = 1, 2,3,4, to the inequality |λ1p1 +λ2p^2/2 +λ3p^2/3+|λ4p^2/4+■(max{p1,p^2/2,p^2/3,p^2/4})-^5/64. This improves the earlier result.
