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December 9th, 2015, 07:42 PM  #1 
Newbie Joined: Dec 2015 From: Virginia Posts: 5 Thanks: 0  Can you all help with with this Pythagorean Triplets/triples question
I have an oral exam next week. I need to be able to explain this to my professor b^2 = [(s^2  t^2)/2]^2 and b^2 = [(s^2 + t^2)/2]^2 Can you all please show me how to distribute these the long way? If this is in the wrong area, can someone move it to the correct area, thanks. 
December 10th, 2015, 04:51 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,852 Thanks: 743 
What are you trying to explain?

December 10th, 2015, 05:56 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,696 Thanks: 2681 Math Focus: Mainly analysis and algebra 
I looks like a method of generating Pythagorean triples as per Joseph H. Silverman's A Friendly Introduction to Number Theory. The book's homepage can be found here.

December 11th, 2015, 10:59 AM  #4  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,340 Thanks: 983 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
December 13th, 2015, 05:08 AM  #5  
Newbie Joined: Dec 2015 From: Virginia Posts: 5 Thanks: 0  Quote:
 
December 13th, 2015, 05:31 AM  #6 
Newbie Joined: Dec 2015 From: Virginia Posts: 5 Thanks: 0 
One more question Where are the "S" and "T" derived from in this formula for finding a Pythagorean Triplet/triple? "So, now that we know what a Pythagorean Triplet is, here is a formula which creates them: Do the following: (1) Choose two integers, s and t, which satisfy: (a) s and t are both odd (b) s>t>0 (2) Then: Let a = st Let b = (s2  t2)/2 Let c = (s2 + t2)/2" 
December 13th, 2015, 06:42 AM  #7 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,696 Thanks: 2681 Math Focus: Mainly analysis and algebra 
That is clearly shown in the document. Since $a^2=c^2b^2=(cb)(c+b)$ and both $(cb)$ and $(c+b)$ are square, we set $s^2=c+b$ and $t^2=cb$.


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