March 16th, 2015, 05:40 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 12:46 AM. 
March 16th, 2015, 10:26 AM  #2 
Senior Member Joined: May 2013 Posts: 118 Thanks: 10 
It might simply mean that a and b are odd, while c is even.
Last edited by skipjack; April 2nd, 2015 at 12:43 AM. 
April 1st, 2015, 09:45 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 12:40 AM. 
April 2nd, 2015, 12:42 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,916 Thanks: 2199 
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. 

Tags 
number theory, pythagorean, triples 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
All Pythagorean Triples c²=a²+b² here  M_B_S  Number Theory  2  July 1st, 2014 11:39 PM 
Pythagorean triples  shunya  Elementary Math  5  June 11th, 2014 10:54 PM 
How many Pythagorean triples?  Pell's fish  Number Theory  3  August 5th, 2011 10:38 AM 
Pythagorean Triples  julian21  Number Theory  2  November 13th, 2010 12:01 PM 
Pythagorean Triples II  julian21  Number Theory  3  November 12th, 2010 11:58 AM 