If a rational number (frac{a}{b}) is a prime number, where (a) and (b) are positive integers, and (b) is not equal to 1, what can we say about the value of (a)?

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Step:1 ：Since (frac{a}{b}) is a rational number, (a) and (b) are integers and (b) is not equal to 0.Step:2 ：Given that (frac{a}{b}) is a prime number, it can only have two distinct positive divisors.Step:3 ：However, if (b) is not equal to 1, then (frac{a}{b}) will have more than two distinct positive divisors, which contradicts the definition of a prime number.Step:4 ：Therefore, the only possibility is that (a) is equal to 0.

Answer

Step: 1 ：Since (frac{a}{b}) is a rational number, (a) and (b) are integers and (b) is not equal to 0.Step: 2 ：Given that (frac{a}{b}) is a prime number, it can only have two distinct positive divisors.Step: 3 ：However, if (b) is not equal to 1, then (frac{a}{b}) will have more than two distinct positive divisors, which contradicts the definition of a prime number.Step: 4 ：Therefore, the only possibility is that (a) is equal to 0.

If a rational number \(\frac{a}{b}\) is a prime number, where \(a\) and \(b\) are positive integers, and \(b\) is not equal to 1, what can we say about the value of \(a\)?

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