April 20th, 2013, 08:48 PM  #1 
Newbie Joined: Apr 2013 Posts: 1 Thanks: 0  Number Theory
Is there a solution to the Diophantine equation (a+b)(c+d)=ab+cd ?

April 20th, 2013, 10:37 PM  #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: Number Theory
Sure, a = b = c = d = 0. Not sure if there are any nontrivial solutions.

April 20th, 2013, 10:54 PM  #3  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Number Theory Quote:
 
April 21st, 2013, 05:50 AM  #4  
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: Number Theory Quote:
 
April 21st, 2013, 07:22 AM  #5 
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: Number Theory
One infinite family: a = b = c = 0.

April 21st, 2013, 11:25 AM  #6 
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: Number Theory
Oh, I suddenly realize that this question may be highly relevant to something I was trying to do many years ago. It's gone take some work finding that stuff again in the clutter of my mind. Kinda like trying to remember whether some document you need is buried somewhere in the cluttered basement, cluttered attic or cluttered garage. Depressing, but it may pop to mind. Anyway, in anticipation of remembering what I was trying to do, I would be eager to see ways of dredging up NONtrivial solutions! 
April 21st, 2013, 12:27 PM  #7  
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: Number Theory Quote:
 
April 21st, 2013, 01:15 PM  #8  
Global Moderator Joined: May 2007 Posts: 6,683 Thanks: 658  Re: Number Theory Quote:
 
April 21st, 2013, 01:27 PM  #9  
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: Number Theory Quote:
 
April 21st, 2013, 01:39 PM  #10  
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: Number Theory Quote:
 

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