Posted by Pythagoras's triple on .
A Pythagorean triple is an ordered triple of positive integers(a,b,c) such that a^2+B^2=c^2.Find
the number of the Pythagorean triples such that all the numbers a,b and c are prime?
for any natural numbers m and n where m and n are relatively prime
2mn, m^2-n^2 and m^2 + n^2 will form a Pythagorean triple.
since the smallest triple is 3,4,5,
one of the numbers (the 2mn) will always be even.
So there are no such Pythagorean triples where all 3 are primes.