Hypothesis Tests · Challenge problem

Test $H_0$: $\mu = 0$ against $H_a$: $\mu > 0$ with $\sigma = 1$, $\alpha = 0.05$ ($z^* = 1.645$). What is the smallest sample size giving power at least $0.90$ when $\mu = 0.5$? (The $z$ with upper tail $0.10$ is $1.282$.)