Not too reduced

Determine the smallest positive integer nn such that 17n+12=x×z17n + 12 = x \times z and n25=y×z n - 25 = y \times z , where x,y, and zx, y, \mbox{ and } z are positive integers, xx and yy are coprime, and both yy and zz are strictly greater than 1.1.

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