How many ordered pairs of positive integers with satisfy ?
Answer and explanation
Correct answer: E.
- Step 1: Since with , must be an integer power of , say with .
- Step 2: Substitute into the equation: , which requires for positive integers and .
- Step 3: The number of positive integer solutions equals the number of divisors of , which is .
Answer
.
Why not the others: incorrectly includes ( or undefined); doubles the factors; counts all exponents instead of divisors; miscounts divisors of 36.
Practise more Powers and roots.
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