Nicolae's polynomial division

Algebra Level 5

P(x)P(x) is a polynomial of degree 7 such that P(2)=35,P(3)=25P(2)=35,\,P(3)=25 and P(5)=23P(5)=23. Let U(x)U(x) be the remainder of P(x)P(x) upon division by (x2)(x3)(x5)(x-2)(x-3)(x-5). Evaluate U(1) U(1) .

This problem is posed by Nicolae S.

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