Question

\(3,4,5\) is a well known primitive pythagorean triple in arithmetic progression. find another primitive pythagorean triple in arithmetic progression

Answer 1

6^2 + 8^2 = 10^2

Answer 2

Nice :) 6,8,10 forms arithmetic progression but is not primitive

Answer 3

I do not know the definition of primitive.

Answer 4

have you heard of this magical thing called google :)
http://www.math.rutgers.edu/~erowland/tripleslist.html

Answer 5

A pythagorean triple (a,b,c) is called primitive if gcd(a,b,c) = 1

Answer 6

did you see the list?

Answer 7

yes :) i don't find any triples in arithmetic progression in that list

Answer 8

*any other primitive triples

Answer 9

However wolf's answer is interesting because it shows (ka, kb, kc) is a pythagorean triple whenever (a,b,c) is a pythagorean triple

Answer 10

i think we have answered it. as you saw there were no arithmetics in the list i showed you, no other primitive tripple contains arithmetics properties other than 3,4,5

Answer 11

looking at the list should be the indicator, i am not about to type out the proof which would involve a series expansion. But if you would like to see use the trusty google