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A Diophantine problemFind all integer solutions of a(a + 1) = b(b + 2). 2 + 2 = 5, for large values of 2. #2 20050810 07:52:23
Re: A Diophantine problemLet's try an example. How about finding b for a=1: "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #3 20050810 09:25:22
Re: A Diophantine probleminteger equations! #4 20050810 10:52:35
Re: A Diophantine problema=0 b=0 #5 20050810 15:56:50
Re: A Diophantine problemIs it possible to use an odds and evens approach ? "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #6 20050810 16:32:35
Re: A Diophantine problemThanks, MathsisFun. Last edited by ganesh (20050810 16:35:20) Character is who you are when no one is looking. #7 20050810 19:10:33
Re: A Diophantine problemThere are no squares that end in 2 or 8, so if 4 +16(4n²+7n+3) always ends in 2 or 8, then we have a proof. Why did the vector cross the road? It wanted to be normal. #8 20050810 19:11:49
Re: A Diophantine problemis it possible to use some general method as outlined by Euclid #9 20050811 09:11:35
Re: A Diophantine problem
But if n = 3 or 4 (mod 5), then 4 + 16(4n²+7n+3) ends in 4. 2 + 2 = 5, for large values of 2. #10 20050811 10:19:18
Re: A Diophantine problemthen, Last edited by wcy (20050811 10:42:04) #11 20050811 10:39:23
Re: A Diophantine problem
Then the LHS equals a² + a + 1. 2 + 2 = 5, for large values of 2. #13 20050811 10:50:55
Re: A Diophantine problem
Or 1. 2 + 2 = 5, for large values of 2. #14 20050816 10:27:33
Re: A Diophantine problemHere is a solution to this one. 2 + 2 = 5, for large values of 2. 