A System of Two Diophantine Inequalities with Primes
Let 1 < d < c < 128 / 119 , 1 < α < β < 6 1 − d / c . In this paper, we prove that there exist positive real numbers N 1 0 and N 2 0 depending on c , d , α , β such that for all real numbers N 1 > N 1 0 , N 2 > N 2 0 and α ≤ N 2 / N 1 d / c ≤ β , the system of two Diophantine inequalities p 1 c + ⋯ + p 6 c − N 1 < N 1 − 1 / c 128 / 119 − c log 109 N 1 , p 1 d + ⋯ + p 6 d − N 2 < N 2 − 1 / d 128 / 119 − d log 109 N 2 is solvable in prime variables p 1 , … , p 6 .
2018 ◽
Vol 7
(1)
◽
pp. 77-83
Keyword(s):
Keyword(s):
2009 ◽
Vol 2009
◽
pp. 1-11
◽
Keyword(s):
2014 ◽
Vol 33
(2)
◽
pp. 59-67
Keyword(s):
2019 ◽
Vol 26
(1/2)
◽
pp. 41-55
◽
2000 ◽
Vol 08
(01)
◽
pp. 1-6
◽
Keyword(s):