March 3rd, 2009, 09:57 AM  #1 
Senior Member Joined: Nov 2007 Posts: 633 Thanks: 0  Diophantine equation
x,y,z,a,b,c integers >1 xy=az + b (1) x+y+z=c (2) a,b,c are known Can we solve the equation? Thank you for any help. 
March 3rd, 2009, 10:17 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Diophantine equation
Yes, it can be solved. xy + ax + ay = ac + b It depends on the factorization of a^2 + ac + b: http://www.alpertron.com.ar/METHODS.HTM#SHyperb 
March 3rd, 2009, 12:24 PM  #3  
Senior Member Joined: Nov 2007 Posts: 633 Thanks: 0  Re: Diophantine equation Quote:
I read it quickly but it seems more complicated case if a, b, and c are big big numbers (300 or 400 digits). We will have a lot of computing work to do before finding any solutions.  
March 3rd, 2009, 12:28 PM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Diophantine equation Quote:
 
March 3rd, 2009, 12:50 PM  #5  
Senior Member Joined: Nov 2007 Posts: 633 Thanks: 0  Re: Diophantine equation Quote:
a,b and c are positive. We do not know for sure if a^2 + ac + b is easily factorizable. Even if .. how to compute all the factors? If a^2 + ac + b is prime? So thanks a lot!!!  
March 3rd, 2009, 03:05 PM  #6 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Diophantine equation
When a^2 + ac + b is prime, it's easy  there are fast checks for numbers with even a thousand digits. But when it has several large factors, it's extremely hard to work with.


Tags 
diophantine, equation 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
diophantine equation, not again!!!  mathbalarka  Number Theory  3  April 23rd, 2012 04:38 AM 
A diophantine equation  maybe?  aSteve641  Number Theory  2  August 1st, 2011 06:27 AM 
Diophantine Equation  Liu997  Number Theory  1  March 25th, 2010 10:13 AM 
A Diophantine equation  duz  Number Theory  8  November 7th, 2008 02:29 PM 
A Diophantine equation  Dacu  Algebra  0  December 31st, 1969 04:00 PM 