Pythagorean Plus One (Posted on 2004-05-17)

	Submitted by Gamer
Rating: 2.0000 (3 votes)
Solution:	(Hide)
All the numbers need to be distinct, so 0 can't equal a, b, or c. The lowest other possibility is a=1, b=a+1=2, which results in a value of c=3. A way to prove that b can be a+1 is posted here: (a^2+1)((a+1)^2+1)= (a^2)(a^2+2a+1)+(a^2)+(a^2+2a+1)+1= (a^4+2a^3+a^2+a^2+a^2+a^2+2a+1)+1= (a^4+ax^3+ax^2+ax+1)+1= (a^2+a+1)^2+1.

	Subject	Author	Date
	The official solution is wrong:	Ady TZIDON	2010-02-23 04:16:13
	Euan seems to be wrong...	Penny	2004-06-05 20:21:35
	re: People seem to be wrong...	Tristan	2004-06-04 18:11:26
	People seem to be wrong...	Euan	2004-06-04 06:37:27
	re: solution	Richard	2004-05-22 21:24:38
	solution	Gururaj	2004-05-22 04:43:22
	no subject	Gururaj	2004-05-21 08:32:02
	re: No Subject	perplexus	2004-05-20 22:06:25
	No Subject	perplexus	2004-05-20 22:02:31
	Pythagorean Minus One	Penny	2004-05-17 18:41:34
	Yet another variation...	Penny	2004-05-17 18:30:09
	re: Maybe a really smart floobler.....	Richard	2004-05-17 14:54:34
	Maybe a really smart floobler.....	Penny	2004-05-17 13:27:00
	re: Hen's eggs	DJ	2004-05-17 12:39:36
	Hen's eggs	Jer	2004-05-17 12:26:56
	All odd Pythagorean Plus One triples	Penny	2004-05-17 10:04:12
	The smallest 4-digit solution.....	Penny	2004-05-17 09:40:33
	solution	derek	2004-05-17 09:23:27
	Solution	Penny	2004-05-17 09:11:09
	Solution??	Oskar	2004-05-17 08:50:36