Posted by **Pythagoras's triple** on Thursday, October 10, 2013 at 10:29pm.

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?

- math -
**Reiny**, Thursday, October 10, 2013 at 11:30pm
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.

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