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## Homework Statement

Let (a, b), (c, d) be in R x R. We define (a, b) ~ (c, d) iff a^2 + b^2 = c^2 + d^2.

Let R* = all positive real numbers (including 0).

Prove that there is a bijection between R* and the set of all equivalence classes for this equivalence relationship.

## Homework Equations

## The Attempt at a Solution

I do not know how the formula for the relationship ~ looks like. I tried mapping from R* x R* -> R* where f: x^2 + y^2 but I got stuck. Any help please?