That \(m\) Under The Radicals

Algebra Level 2

There exists a unique positive integer \(m\) such that \[ \quad \left(1+\sqrt{m}\right)^n=2\left(1+\sqrt{m}\right)^{n-1}+\left(1+\sqrt{m}\right)^{n-2} \] is an identity. Find \(m\).

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