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Let \(\alpha\) and \(\beta\) be two natural numbers and \(n = 2^{\alpha} \times 3^{\beta}\).
The number of divisors of \(n^2\) is three times the number of divisors of \(n\).
Prove that \((\alpha - 1)(\beta - 1) = 3\).
Deduce the possible values for \(n\).
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