what is Pythagorean triplet?
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A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². Such a triple is commonly written, and a well-known example is. If is a Pythagorean triple, then so is for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime.
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Pythagorean triple consists of three positive integers a, b, and c, such that
a² + b² = c².
- The square of the length of the hypotenuse of a right triangle is the sum of the squares of the lengths of the two sides. This is usually expressed as a2+b2 = c2.
- Integer triples which satisfy this equation are Pythagorean triples. The most well known examples are (3,4,5) and (5,12,13).
Example: The smallest Pythagorean Triple is 3, 4 and 5.
Let's check it:
32 + 42 = 52
Calculating this becomes:
9 + 16 = 25
Yes, it is a Pythagorean Triple!
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