Fan & Medal
4) Use the Polynomial Identity below to help you create a list of 10 Pythagorean Triples:
(x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2
Hint #1: c^2 = a^2 + b^2
Hint #2: pick 2 positive integers x and y, where x y

Question

Fan & Medal
4) Use the Polynomial Identity below to help you create a list of 10 Pythagorean Triples:
(x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2
Hint #1: c^2 = a^2 + b^2
Hint #2: pick 2 positive integers x and y, where x > y

anonymous · Answer

Would I be able to just list any 10 Pythagorean triples?

anonymous · Answer

I think you can pick  x=2 and y=1,   then x=3 and y=1, then x=3 and y=2

Things like that and it will give you the tripples

anonymous · Answer

What?

anonymous · Answer

If you let x=2 and y=1, you get: $$
(2^2+1^2)^2 = (2^2-1^2)^2+(2(2)(1))^2 \implies 5^2=3^2+2^2
$$This is  your first Pythagorean tipple.

anonymous · Answer

Ohhhh, that clears up a lot. Thanks. I'll start doing it and post what I get to see if it's right.

anonymous · Answer

Wait, I thought the lowest Pythagorean triple was 3,4,5?