Mysterious polynomial

Number Theory Level 4

A polynomial \(f(x)\) with positive integer coefficients satisfies \(f(1)= 12\) and \(f(12)=2080\). Find the last three digits of \(f(10)\).

Details and assumptions

  • We are talking about all the numbers in their decimal representations.

  • You aren't given any information about the degree of the polynomial, except that it is positive.


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