Find the value of \( z \) for which \( \frac{z}{2+i} \) is prime and minimal.
15 words

The minimal prime value of \( z \) for \( \frac{z}{2+i} \) is \( z = 5 + i \).

Find the value of \( z \) for which \( \frac{z}{2+i} \) is prime and minimal.

Discover the minimal prime value of \( z \) for which \( \frac{z}{2+i} \) is prime, with a step-by-step solution. This complex numbers problem involves prime numbers in the Gaussian integers and division of complex numbers. Ideal for students at the undergraduate level.

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