Polynomial Terms Puzzle

Algebra Level 3

Let $P(X)$ be a hidden polynomial of finite degree $N$ :

$P(X) = a_N X^{N} + a_{N-1} X^{N-1} + ... + a_1 X + a_0$

where all terms $\forall a_i \in \mathbb{N}$ .

You do not know $N$ . You can make as many queries as you want for $P(c)$ with $c \in \mathbb{Q}$ of you choice and get the result.

How many queries are needed to know every $a_i$ ?

N-1 3 N 0 N-2 1 2

1 solution

Florent Periat
Oct 11, 2019

You first start with $P(1)$ and get the result $B$ . Then you ask for $P(B) = R$ .

You can get the $a_i$ with changing $R$ in base $B$ !

So answer is 2.