If you've worked with the Pythagorean Theorem, you've come across some integer solutions.

3-4-5 and 5-12-13 come to mind, especially if you've studied for the SAT; 8-15-17 is another good one.

How many can you find?

Which one is your favorite?

Is there a way to find as many as you want?

(For those who haven't seen this trivia snippet)

pick distinct positive integer values for u and v: perhaps 3 and 4.

The three sides are 2*u*v, u² + v², and |u² - v²|, thus 24, 25, 7

The hypotenuse is simply the longest of the three sides, but won't be generated by the same expression all the time.

Those interested in this topic will want to get a copy of Waclaw Sierpinski's "Pythogrean Numbers", which was reprinted by Dover Publications in 2003:

ReplyDeletehttp://www.amazon.com/dp/0486432785#reader_0486432785

This is a beautifully written book (currently costs $10.67) that anyone from a good high school student to a math professor will find things that are both understandable and interesting.

Sierpinski is better known for his extensive research in various areas of set theory, but nonetheless he still managed to publish over 100 papers and 13 books in number theory.