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CTK Exchange
Ravin T'pillai
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Feb-06-05, 09:46 AM (EST) |
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"Trouble With Pythagorean Triples"
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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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alexb
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
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>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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