The present paper proved that if λ1, λ2, λ3 are positive real numbers, λ1/λ2 is irrational. Then, the integer parts of λ1x12＋ λ2x22＋ λ3x34 are prime infinitely often for natural numbers x1, x2, x3.
We show that if λ1 , λ2 , λ3 are non-zero real numbers, not all of the same sign, η is real and λ1 /λ2 is irrational, then there are infinitely many ordered triples of primes (p1 , p2 , p3 ) for which |λ1 p1 + ...We show that if λ1 , λ2 , λ3 are non-zero real numbers, not all of the same sign, η is real and λ1 /λ2 is irrational, then there are infinitely many ordered triples of primes (p1 , p2 , p3 ) for which |λ1 p1 + λ2 p2 + λ3 p2 3 + η| < (max pj )- 1/40 (log max pj ) 4 .展开更多
In this paper, we give a necessary and sufficient solvable condition for diagonal cubic equation with prime variable in arithmetic progressions and the outline of the proof.
文摘The present paper proved that if λ1, λ2, λ3 are positive real numbers, λ1/λ2 is irrational. Then, the integer parts of λ1x12＋ λ2x22＋ λ3x34 are prime infinitely often for natural numbers x1, x2, x3.
基金Supported by the NNSF of China(11071070)Supported by the Science Research Plan of Education Department of Henan Province(2011B110002)
文摘We show that if λ1 , λ2 , λ3 are non-zero real numbers, not all of the same sign, η is real and λ1 /λ2 is irrational, then there are infinitely many ordered triples of primes (p1 , p2 , p3 ) for which |λ1 p1 + λ2 p2 + λ3 p2 3 + η| < (max pj )- 1/40 (log max pj ) 4 .
基金Supported by the National Natural Science Foundation of China(10471104)
文摘In this paper, we give a necessary and sufficient solvable condition for diagonal cubic equation with prime variable in arithmetic progressions and the outline of the proof.
