Diophantine approximation with one prime and three squares of primes

摘要

Abstract Let λ 1 , … , λ 4 be non-zero real numbers, not all of the same sign, with λ 1 / λ 2 irrational, and ? be a real number. We prove that for any ε 0 , the inequality | λ 1 p 1 + λ 2 p 2 2 +