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Diophantine approximation with two primes and one square of prime. (English) Zbl 1274.11111
Summary: We show that if $$\lambda_1,\lambda_2,\lambda_3$$ are non-zero real numbers, not all of them are the same sign, $$\eta$$ is real and $$\lambda_1/\lambda_2$$ is irrational, then there are infinitely many ordered triples of primes $$(p_1, p_2, p_3)$$ for which $$|\lambda_1p_1+\lambda_2p_2+\lambda_3p_3^2+\eta|<(\max p_j)^{-\frac 1{40}}(\log \max p_j)^4$$.

##### MSC:
 11J25 Diophantine inequalities