Pythagorean Triples Formula – Problem Solution with Solved Example

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Pythagorean Triples Formula

Till the time, we have heard of Pythagorean theorem. Here, we will discuss the concept of Pythagorean triples and the related formula for the same. A Pythagorean triplet is consisting of three positive integers that could be given as the a, b, and c. In that case (a, b, c) would be a Pythagorean triplet for any integer k. There is one specific category where primitive Pythagorean triple is given as co-primes a, b and c. 

\[\large c^{2}=a^{2}+b^{2}\]

Do you know what is a co-prime number? A co-prime number is the number that has no divisor larger than one. If there is some triangle based on the concept of Pythagorean triple then it is called as the Pythagorean triangle, and is necessarily a right triangle.

Obviously, this name has been taken from Pythagorean theorem where one side is always aligned at the right angle and Pythagorean triples are also based on the same concept. At the same time, if there is one right-angle triangle with non-integer sides then it does not form any Pythagorean triples.

Pythagorean triples are into existence since the ancient times from 1800 BC or more. However, the concept became clearer after 1900 when it was used practically. When you search something for integer solution then this is a Diophantine equation.

We can say that Pythagorean triples are one of the oldest known solutions in the case of a nonlinear Diophantine equation. To understand the concept it depth, you need to practice this formula continuously and get hands-on expertize on the same.