Ask an opponent to choose a polynomial p(x) with nonnegative integer coefficients (of any degree). Tell him you can determine what it is (degree and coefficients) with just two values: you choose a and ask for p(a), then choose b and ask for p(b). What is a winning strategy?

Ask for p(ð) or some such non-algebraic number.

In the example p(x)=(5x²+6x+2)

p(ð)= 5ð²+6ð+2

Since this is the only reasonable way of expressing the value, you have the solution with only one value.

 

Posted by Jer on 2005-06-14 17:25:58