Assume that $P(x)$ is a polynomial with integer non negative coefficients, different from constant. Baron Munchausen claims that he can restore $P(x)$ provided he knows the values of $P(2)$ and $P(P(2))$ only. Is the baron's claim valid?
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Tags: algebra, polynomial, algebra unsolved, Baron Munchausen
RSM
09.02.2011 12:06
I think he is true. Value of P(2) is greater than each of the coefficients of the polynomial So if we represent P(P(2)) with base P(2) then the digits in the representation are corresponding values of the co-efficients of the polynomial. It holds for any P(n) and P(P(n)) for natural number n
myro111
09.02.2011 16:10
RSM wrote: I think he is true. Value of P(2) is greater than each of the coefficients of the polynomial So if we represent P(P(2)) with base P(2) then the digits in the representation are corresponding values of the co-efficients of the polynomial. It holds for any P(n) and P(P(n)) for natural number n Yes that is true.That is a very interesting problem.
AlphaBetaTheta
11.08.2011 02:19
Can someone give a legitimate solution to this question?
Sampro
24.03.2014 17:51
Very interesting problem. Here is the solution.