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Determine the smallest positive integer nnn such that 17n+12=x×z17n + 12 = x \times z 17n+12=x×z and n−25=y×z n - 25 = y \times z n−25=y×z, where x,y, and zx, y, \mbox{ and } zx,y, and z are positive integers, xxx and yyy are coprime, and both yyy and zzz are strictly greater than 1.1.1.
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