Apythagorean triple is a triple of natural numbers satisfying the equation a^2+b^2+c^2.
one way to produce a pythagorean triple is to add the reciprocals of any two consecutive even or odd numbers. for example, 1/5+1/7=12/35. now 12^2+35^2=1369. this is a pythagorean triple if 1369 is a perfect square, which it is since 1369=37^2. so 12, 35, 37 is a pythagorean triple. prove that this method always works.