The exceptional set for Diophantine inequality with mixed powers of primes

Yu Fu, Linzhu Fu, Liqun Hu

Assume that $\hat{I}{»}_1,\hat{I}{»}_2,\hat{I}{»}_3,\hat{I}{»}_4,\hat{I}{»}_5,\hat{I}{»}_6,\hat{I}{»}_7$ are non-zero real numbers , $\hat{I}{»}_1/\hat{I}{»}_2$ is an irrational number. Let $\mathcal{V}$ be a well-spaced sequence, and $\hat{I}´>0$. For an…