How can we use Hilbert's theorem 90 to find all Pythagorean triples?

Expert Solution

Answer.

Using Hilbert’s theorem 90, we can find all Pythagorean triples, i.e. rational
points on the circle x
x^2+y^2=1.

Let a, b be rational numbers s.t. a^2+b^2=1

Then there exists
c, d ∈ Z s.t.

Let a, b be rational numbers s.t. a^2 + Db^2 = 1. Then there exists
c, d ∈ Z s.t.

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Thank you.

Colby Messinger answered 1 year ago

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