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Pythagorean Plus One (Posted on 2004-05-17) Difficulty: 3 of 5
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?

See The Solution Submitted by Gamer    
Rating: 2.5000 (2 votes)

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re: People seem to be wrong... | Comment 18 of 20 |
(In reply to People seem to be wrong... by Euan)

A "Pythagorean Plus One" triple is not defined as being a pythagorean triple.  It may seem to imply that it is a pythagorean triple by the name, but it doesn't, that's just what Gamer chose to name it.

As for a triple that is both a "pythagorean plus one" triple and a pythagorean triple, I think it is impossible.

a*b=c
a^2+b^2=c^2
(a*b)^2=a^2+b^2
0=a^2+b^2+^2b^2
0=(b^2+1)a^2+b^2
a=(0+/-sqrt(0-4b^2(b^2+1)))/2
Notice that in the above line, there is no positive real solution for both a and b.

Edit: Fixed sqrt sign and sqr signs

Edited on June 4, 2004, 10:33 pm
  Posted by Tristan on 2004-06-04 18:11:26

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