Pythagorean Triples - Maple Help
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Pythagorean Triples

Main Concept

A Pythagorean triple consists of three positive integers, , ,  and  such that .

 

These triples are usually denoted as . The simplest and most common triple is .

 

Euclid's formula can be used to generate a Pythagorean triple given an arbitrary pair of positive integers  and  where  :

 

Primitive Triples(PPT)

If , , and  are mutually prime or co-prime, the triple is known as a primitive. A primitive triple has many special properties such as:

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.

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 is always a perfect square.

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At most one of , ,  is a square.

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Exactly one of ,  is odd;  is odd.

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Exactly one of ,  is divisible by 3.

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Exactly one of ,  is divisible by 4.

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Exactly one of , ,  is divisible by 5.

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The area   is an even number.

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By definition,  is also congruent, that is, a positive integer which is the area of a right angled triangle with rational numbered side lengths.

 

Adjust the sliders or type positive integers in the boxes to change m and n and create the various Pythagorean triples.

 

Note: If  the computer will make . If , no triangle can be formed.

 

 

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