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Subject: "Trouble With Pythagorean Triples"     Previous Topic | Next Topic
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Ravin T'pillai
guest
Feb-06-05, 09:46 AM (EST)
 
"Trouble With Pythagorean Triples"
 
   On this site there is an article about Pythagorean Triples. It'says that where n and m are intergers n>m. It says the middle side can be expressed 2nm. If n and m are integers, then nm must also obviously be an integer, which I will call X. Hence, 2nm = 2x. 2x therefore, (as x is an integer) must be even. However, in the triple

8, 15, 17
This is not the case.How then can 2nm = 15??
Moreover,

Can 6 be expressed as the difference between 2 squares? The only Integers that six can be divided by to give another integer are:
1, 2, 3 and 6,

Hence : (x + y) = 3 or 6
(x - y) = 2 or 1
What are the solutions to x and y here??
Thank you; Ravin


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alexbadmin
Charter Member
1449 posts
Feb-06-05, 10:04 AM (EST)
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1. "RE: Trouble With Pythagorean Triples"
In response to message #0
 
   >On this site there is an article about Pythagorean Triples.
>It'says that where n and m are intergers n>m. It says the
>middle side can be expressed 2nm. If n and m are integers,
>then nm must also obviously be an integer, which I will call
>X. Hence, 2nm = 2x. 2x therefore, (as x is an integer) must
>be even. However, in the triple
>
>8, 15, 17
>This is not the case.How then can 2nm = 15??

In the article you refer to a = n2 - m2, b = 2nm. Thus your triple should be written as

15, 8, 17

with no apparent contradiction.

>Moreover,
>
>Can 6 be expressed as the difference between 2 squares? The
>only Integers that six can be divided by to give another
>integer are:
>1, 2, 3 and 6,
>
>Hence : (x + y) = 3 or 6
> (x - y) = 2 or 1

x+y and x-y are of the same parity.

>What are the solutions to x and y here??


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