My Math Forum Formula for all and only primitive Pythagorean triples.

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January 19th, 2014, 07:53 AM   #11
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Re: Formula for all and only primitive Pythagorean triples.

Quote:
 Originally Posted by complicatemodulus As probably already written here I found more interesting that: Given an odd integer A there are ALWAYS two integer B and C that satisfy: A^2 = C^2-B^2 If you keep: A, B= (A^2-1)/2, C= (A^2+1)/2 so you can see all triplets sorted by A odds. To obtain triple for ALL integers you've just to ADD the even 2*A values where A is what above. Thanks Ciao S.
Gonna say same thing :P Learnt it very young from murderous maths

 January 19th, 2014, 09:54 PM #12 Banned Camp   Joined: Dec 2012 Posts: 1,028 Thanks: 24 Re: Formula for all and only primitive Pythagorean triples. Very sorry I rewrite with more care: A1) Given an odd integer A, there are ALWAYS two integers B and C that satisfy: A^2 = C^2-B^2 If you keep: A, B= (A^2-1)/2, C= (A^2+1)/2 so you can see all triplets sorted by A odds. A2) To obtain triplets for ALL even integers you've to keep for A even: A, B= [(A/2)^2 ]-1, C= [(A/2)^2 ]+1 so you can see all triplets sorted by A even. With this 2 formulas you will obtain a triplet for any A from A=1 to infinite. Thanks & sorry Ciao S.

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