I m not able to understand this formula (2m,m^2-1,m^2+1)

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Solution

It is the pythagorean triplet formula - (2m),(m^2 - 1),(m^2 + 1).

Triple comes right from the Pythagorean Theorem which states that for all integers a, b, and c, c²= a² + b²

Example

5² + 12² = 13²

The triple is (5, 12, 13)
Definition: Integers a, b, and c, such that a² + b²= c^2.

Plato, a Greek Philosopher, came up with a great formula for finding Pythagorean Triples

Plato's formula for Pythagorean Triples: (2m)² + (m² - 1)² = (m² + 1)²

To get a triple, just let m be any positive integer and do the math.

Let m = 2 for instance, we get:

(2m)² + (m² - 1)² = (m² + 1)²

(2× 2)² + (2² - 1)² = (2² + 1)²

(4)² + (4 - 1)² = (4 + 1)²

(4)² + (3)² = (5)²

Thus, the Pythagorean triple is (3, 4, 5)

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