Question

A = x2 : x belong to I and -8 < =X <= 8n​

Answer 1

Answer:

I don't now sorry check others

Answer 2

I showed that by taking any Pythagorean triple x2+y2=z2 and multiplying by z2(n−1) we get (zn−1x)2+(zn−1y)2=(z2)n, which allows me to generate solutions easily for any value of n. I managed to find several similar questions on this site, such as this one concerning the specific case n=3. I notice that all of these questions take a similar approach and start with a Pythagorean triple and use it to generate general solutions.

I showed that by taking any Pythagorean triple x2+y2=z2 and multiplying by z2(n−1) we get (zn−1x)2+(zn−1y)2=(z2)n, which allows me to generate solutions easily for any value of n. I managed to find several similar questions on this site, such as this one concerning the specific case n=3. I notice that all of these questions take a similar approach and start with a Pythagorean triple and use it to generate general solutions.Is there a way to prove the statement (or better yet provide solutions to the equation) without first relying on Pythagoras?