#2**+5 **

**What is a pythagorean triple **

**https://commons.wikimedia.org/wiki/File:Pythagorean.svg#/media/File:Pythagorean.svg**

A Pythagorean triple consists of three positive integers *a*, *b*, and *c*, such that *a*^{2} + *b*^{2} = *c*^{2}. Such a triple is commonly written (*a*, *b*, *c*), and a well-known example is (3, 4, 5). If (*a*, *b*, *c*) is a Pythagorean triple, then so is (*ka*, *kb*, *kc*) for any positive integer *k*.

Generating a triple:

A fundamental formula for generating Pythagorean triples given an arbitrary pair of positive integers *m* and *n* with *m* > *n*. The formula states that the integers

$$a = m^2 - n^2 ,\ \, b = 2mn ,\ \, c = m^2 + n^2$$

or

$$a = k\cdot(m^2 - n^2) ,\ \, b = k\cdot(2mn) ,\ \, c = k\cdot(m^2 + n^2)$$

form a Pythagorean triple.

Example:

$$\\ \text{If } m=2 \text{ and } n = 1:\\

a= 2^2-1^2 =4 - 1 = 3 \\

b = 2\cdot 2 \cdot 1 = 4 \\

c = 2^2 + 1^2 = 4+1=5$$

Pythagorean triple (3, 4, 5), because $$\small{\text{$3^2+4^2=5^2$}}$$

heureka
Apr 22, 2015

#1**+5 **

A Pythagorean Triple is a group of three numbers that satisfy the Pythagorean Theorem, a^2+b^2=c^2.

Examples would be 3-4-5,6-8-10,7-24-25,8-15-17,16-30-34... you get the idea.

There's an infinite amount of Pythagorean Triples, though.

DarkBlaze347
Apr 21, 2015

#2**+5 **

Best Answer

**What is a pythagorean triple **

**https://commons.wikimedia.org/wiki/File:Pythagorean.svg#/media/File:Pythagorean.svg**

A Pythagorean triple consists of three positive integers *a*, *b*, and *c*, such that *a*^{2} + *b*^{2} = *c*^{2}. Such a triple is commonly written (*a*, *b*, *c*), and a well-known example is (3, 4, 5). If (*a*, *b*, *c*) is a Pythagorean triple, then so is (*ka*, *kb*, *kc*) for any positive integer *k*.

Generating a triple:

A fundamental formula for generating Pythagorean triples given an arbitrary pair of positive integers *m* and *n* with *m* > *n*. The formula states that the integers

$$a = m^2 - n^2 ,\ \, b = 2mn ,\ \, c = m^2 + n^2$$

or

$$a = k\cdot(m^2 - n^2) ,\ \, b = k\cdot(2mn) ,\ \, c = k\cdot(m^2 + n^2)$$

form a Pythagorean triple.

Example:

$$\\ \text{If } m=2 \text{ and } n = 1:\\

a= 2^2-1^2 =4 - 1 = 3 \\

b = 2\cdot 2 \cdot 1 = 4 \\

c = 2^2 + 1^2 = 4+1=5$$

Pythagorean triple (3, 4, 5), because $$\small{\text{$3^2+4^2=5^2$}}$$

heureka
Apr 22, 2015