50 followers question
I am thinking of a polynomial in of degree 10 with non-egative integer coefficients. You can ask me the value of the polynomial at any value of , and I will tell you. Then you can do this again, as many times as you like. How many questions do you have to ask to determine what my polynomial is?
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1 solution
The first question you would need to ask is, "What is f ( 1 ) ?" This gives the sum of the coefficients of the polynomial. Because the coefficients are non-negative, we know that the largest coefficient is no more than f ( 1 ) . Next, we choose a number larger than f ( 1 ) (call it k ) and ask "What is f ( k ) ?" After we're given an answer, we can convert that result into base k . The n th block will give us the coefficient of x n .