#1**+5 **

There are an infinite number of such numbers!

For example, a=3, b=4 and c=5 satisfy a^{2} + b^{2} = c^{2 }

But if you multiply a, b and c by the same number, say, n then you will find that the numbers a=3n, b=4n and c=5n also satisfy a^{2} + b^{2} = c^{2}

.

Alan
May 16, 2015

#2**+5 **

I know pretty much nothing on Pythagoras.

But i remember watching a video, is it that A= triangle numbers

b= even

c=prime

its probably wrong like i said i know nothing about it.

But i'm sure its for right and triangles?

MathsGod1
May 16, 2015

#3**+5 **

**Hi MathsGod1**

**Here is a video you should watch and absorb :)**

**https://www.khanacademy.org/math/geometry/right_triangles_topic/pyth_theor/v/pythagorean-theorem**

**----------------------------------**

Oh I almost forgot. Numbers that work for the pythagorean Theorem are called **pythagorean triads.**

Melody
May 17, 2015

#4**+5 **

**what is the numbers that satisfies the pythagoras theorem ?**

**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
May 17, 2015