IMO 1966 LL BUL12

Find digits x, y, z such that the equality

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IMO 1966 LL BUL12

Origin: BUL

Problem

Find digits x, y, z such that the equality \sqrtxx \cdot \cdot \cdot x    2n −yy \cdot \cdot \cdot y    n = zz \cdot \cdot \cdot z    n holds for at least two values of n \inN, and in that case find all n for which this equality is true.