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\(P(x)\) is a polynomial of degree 7 such that \(P(2)=35,\,P(3)=25\) and \(P(5)=23\). Let \(U(x)\) be the remainder of \(P(x)\) upon division by \((x-2)(x-3)(x-5)\). Evaluate \( U(1) \).

This problem is posed by Nicolae S.

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