
Math General Math Forum  For general math related discussion and news 
 LinkBack  Thread Tools  Display Modes 
June 2nd, 2017, 12:37 PM  #1 
Newbie Joined: Jun 2017 From: United Kingdom Posts: 1 Thanks: 0  Primitive Pythagoras nth term
Hi new to this forum. I was messing about with generating pythagorean triples using: x^2y^2,2xy,x^2+y^2 and the difference between b and c and noticed this. I knew that if x1=y b would be 1 less than c. I realised this meant you could organise these triples using x=n+1 and y=n but realised that for triples where b+2=c the nth term would look like this: x= [(2n+3)2^0.5]/2 and y=[(2n+1)2^0.5]/2 these always make primitive triples and I was wondering whether anyone knew if it could be done for places where there is different gaps between b and c. Thanks. Last edited by greg1313; June 2nd, 2017 at 12:47 PM. 
June 3rd, 2017, 08:42 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
These 7 Pythagorean triples all have shorter leg = 660: 660,779,1021 660,989,1189 660,2989,3061 660,4331,4381 660,12091,12109 660,27221,27229 660,108899,108901 Also, that is the only case where short leg < 1000. Perhaps that'll help you in "checking different gaps". 
June 3rd, 2017, 09:41 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra 
If you use $a=mn, \, b=\frac12(m^2n^2), \, c=\frac12(m^2+n^2)$, then every coprime pair $(m,n)$ of odd natural numbers gives you a primitive Pythagorean Triple. Furthermore, this scheme gives you every primitive Pythagorean Triple.


Tags 
nth, primitive, pythagoras, term 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Sequence  Term to term help required  Hardup  New Users  3  April 30th, 2016 10:12 AM 
using pythagoras theorem (2)  tanz10  Geometry  3  February 17th, 2015 08:40 AM 
using pythagoras theorem  tanz10  Geometry  1  February 15th, 2015 07:52 AM 
PYTHAGORAS COORDINATES  stevembe  Algebra  10  September 23rd, 2013 08:25 AM 
Term by term differentiation  forcesofodin  Real Analysis  4  August 14th, 2010 05:50 PM 