2024 AMC 10 Problems/Problem 15
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Problem
Let , , and be positive integers such that . What is the least possible value of such that , , and form a non-degenerate triangle?
Solution
We know that represents a Pythagorean triple. The smallest Pythagorean triple is .
To check if this forms a non-degenerate triangle, we verify the triangle inequality:
All inequalities hold, so is a valid solution.
Therefore, the least possible value of is .