March 16th, 2015, 06:40 AM  #1 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36  Pythagorean Triples
I'm starting my journey of 'number theory' by reading A Friendly Introduction to Number Theory (4th Edition) (Featured Titles for Number Theory): Joseph H. Silverman: 9780321816191: Amazon.com: Books . I'm in the chapter 2 which is Pythagorean Triples. I don't understand. It says there are numbers x,y and z such that $$a=2x+1,$$ $$b=2y+1$$ and $$c=2z.$$My problem is how these equations come? Last edited by skipjack; April 2nd, 2015 at 01:46 AM. 
March 16th, 2015, 11:26 AM  #2 
Senior Member Joined: May 2013 Posts: 115 Thanks: 10 
It might simply mean that a and b are odd, while c is even.
Last edited by skipjack; April 2nd, 2015 at 01:43 AM. 
April 1st, 2015, 10:45 PM  #3 
Member Joined: Apr 2015 From: india Posts: 83 Thanks: 0 Math Focus: pi,prime numbers,random function 
121 + 9 = 130 = 81 + 49, what about 130?
Last edited by skipjack; April 2nd, 2015 at 01:40 AM. 
April 2nd, 2015, 01:42 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,104 Thanks: 1907 
As 130 is not a perfect square, a Pythagorean triple (a, b, c) cannot have (a, b) = (11, 3) or (9, 7). The book states "Next, suppose that a and b are both odd, which means that c would have to be even." That's why the book uses integers x, y and z in the way posted above. 

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number theory, pythagorean, triples 
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