Algebraic number

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An algebraic number is a root of a polynomial with integer coefficients. Examples include $\frac{1}{3}$, $\sqrt{2}+\sqrt{3}$, $i$, and $\frac{4+\sqrt[27]{19}}{\sqrt[3]{4}+\sqrt[7]{97}}$. A number that is not algebraic is called a transcendental number. Examples of transcendental numbers are $e$ and $\pi$.

Algebraic numbers are studied extensively in algebraic number theory.

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