摘要
Suppose that λ_(1),…,λ_(5) are nonzero real numbers,not all of the same sign,satisfying that λ_(1)/λ_(2) is irrational.Then for any given real number η and ε>0,the inequality |λ_(1)p_(1)+λ_(2)p_(2)^(2)+λ_(3)p_(3)^(3)+λ_(4)p_(4)^(4)+λ_(5)p_(5)^(5)+η|<(max_(1≤j≤5)p_(j)^(j))^(-19/756+ε) has infinitely many solutions in prime variables p_(1),…,p_(5).This result constitutes an improvement of the recent results.
