Qurak

AlgebraicNumberDenominator

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Smallest positive integer whose product with the number is an algebraic integer

AlgebraicNumberDenominator[a]
AlgebraicNumberDenominator[1 / Sqrt[3]] → 3AlgebraicNumberDenominator[(1 + Sqrt[5]) / 2] → 1AlgebraicNumberDenominator[Root[5 - 6#1 + 3#1 ^ 3 &, 1]] → 3

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