
Number Theory Number Theory Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 8th, 2017, 05:01 PM  #1 
Newbie Joined: Jan 2017 From: Mangalore, Karnataka, India Posts: 11 Thanks: 0  Integer solutions to (x^2 + x + 2) + (y^2 + y + 2) = (z^2 + z + 2)?
Whether there is any Integer solution to (x^2 + x + 2) + (y^2 + y + 2) = (z^2 + z + 2)?

January 8th, 2017, 06:24 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,285 Thanks: 439 Math Focus: Yet to find out. 
What happens if x=y Sent from my iPhone using Tapatalk 
January 8th, 2017, 06:52 PM  #3  
Member Joined: Dec 2016 From: USA Posts: 46 Thanks: 11  Quote:
$$(x^2 + x + 2) + (y^2 + y + 2) = (z^2 + z + 2)$$ has infinitely many integer solution triples (x,y,z). Here's one class of solutions: \begin{align*} x &= n\\ y &= \frac{n(n+1)}{2}\\ z &= \frac{n^2+n+2}{2}\\ \end{align*} where n is an arbitrary integer.  
January 8th, 2017, 07:18 PM  #4 
Newbie Joined: Jan 2017 From: Mangalore, Karnataka, India Posts: 11 Thanks: 0 
Is there any general method to find integer solutions to (ax^2+bx+c) + (ay^2+by+c) = (az^2+bz+c) ?

January 8th, 2017, 08:10 PM  #5 
Newbie Joined: Jul 2015 From: tbilisi Posts: 26 Thanks: 7 
Need the formula in General? It is very bulky. Decisions are determined using the equation Pell. For some special case solution is always there and the formula is as follows. diophantine equations  Curves triangular numbers.  Mathematics Stack Exchange 

Tags 
integer, solutions 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Integer solutions to (x^2+x) + (y^2+y) = (z^2+z)  Naveenchandra Kumar  Algebra  4  January 9th, 2017 11:03 AM 
Integer Solutions to ZēsZ+p=0  AlephUser  Elementary Math  0  January 3rd, 2014 05:42 AM 
Integer solutions  proglote  Number Theory  4  June 8th, 2011 01:41 PM 
all integer solutions of 3^m2^n=+1  calligraphy  Number Theory  7  April 13th, 2011 12:56 PM 
x^5+31=y^2 has no integer solutions  elim  Number Theory  4  April 5th, 2010 01:05 PM 