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)?

Question

Accepted 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.

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 $a$ ?

Answer

Popular Problems

If a rational number ab 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?

Answer

Popular Problems

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 $a$ ?