Not too reduced

Number Theory Level 4

Determine the smallest positive integer \(n\) such that \(17n + 12 = x \times z \) and \( n - 25 = y \times z \), where \(x, y, \mbox{ and } z\) are positive integers, \(x\) and \(y\) are coprime, and both \(y\) and \(z\) are strictly greater than \(1.\)