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Explanation with Examples: Finite Subgroup of Rational Numbers Modulo Squares and Its Elements

Let $\mathbb Q^{\times}/\mathbb Q^{\times^2}$ denote the group of rational numbers modulo squares. This means that we regard two nonzero rational numbers $x_1, x_2$ as equivalent if the ratio $x_1/x_2$...
Consider Non-Trivial Cases's user avatar