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# what is the numbers that satisfies the pythagoras theorem

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what is the numbers that satisfies the pythagoras theorem?

Guest May 16, 2015

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Wow, thanks herueka and Melody, I shall visit the links!

MathsGod1  May 17, 2015
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There are an infinite number of such numbers!

For example, a=3, b=4 and c=5 satisfy a2 + b2 = c

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 a2 + b2 = c2

.

Alan  May 16, 2015
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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
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Hi MathsGod1

Here is a video you should watch and absorb :)

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

Melody  May 17, 2015
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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 a2 + b2 = c2. 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
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