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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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Some Thoughts Solution?? | Comment 1 of 20
If you write a=x^2+1, b=y^2+1, c=z^2+1, then if c=ab we find that x^2y^2+x^2+y^2 = z^2 and we can write z^2-x^2y^2 = x^2+y^2, or (z+xy)(z-xy)=x^2+y^2.

Plugging in the classic x=3, y=4, we find that z=13, so a=10, b=17, c=170.

  Posted by Oskar on 2004-05-17 08:50:36
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