AMC 10B 2024 (Problem 13)
Positive integers and satisfy the equation . What is the minimum possible value of ?
Squaring both sides gives
Since and are integers, is an integer. Therefore, is rational, so is a perfect square. Thus, and have the same squarefree part. Since , their common squarefree part must be .\n\nTherefore,
where and are positive integers satisfying .
Since , the minimum of occurs when and are as close as possible to each other.
Thus, and (or vice versa).
(B)