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 Pythagorean Plus One (Posted on 2004-05-17)
A "Pythagorean Plus One" triple can be defined as any three distinct integers a, b, c, such all three of these are one more than a perfect square, and also a times b equals c. What is the lowest value of c possible?

 Submitted by Gamer Rating: 2.5000 (2 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

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