The Pythagoreans were students of Pythagoras' school of thought.They subscribed to Pythagoreanism,a philosophy that was dominated by mathematics and mysticism.
A Pythagorean triple consists of three positive integers such that
A triple is said to be primitive if , and are co-prime to each other( ).
There are primitive triples with and as shown below.
Find the number of primitive Pythagorean triples with and ?
Details and assumptions
- You may assume that the triplets and are the same when counting.
- This was inspired by a projecteuler problem
- For more about Pythagoreans and irrational numbers take a look at Peter's note on the discovery of irrational numbers.
- There is a great interactive tutorial on pythagorean triples here.