3 How many ordered pairs of positive integers (a, b) are there such that a right triangle with legs of length a, b has an area of p, where p is a prime number less than 100?

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Hugo Barnes

Mathematics

5 November, 08:05

3 How many ordered pairs of positive integers (a, b) are there such that a right triangle with legs of length a, b has an area of p, where p is a prime number less than 100?

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Boston Donaldson · Answer 1

The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a2 + b2 = c2; thus, Pythagorean triples describe the three integer side lengths of a right triangle.