MathDB

Alice and Bob are stuck in quarantine, so they decide to play a game. Bob will write down a polynomial

f(x)

with the following properties:
(a) for any integer

n

f(n)

is an integer; (b) the degree of

f(x)

is less than

187

.
Alice knows that

f(x)

satisfies (a) and (b), but she does not know

f(x)

. In every turn, Alice picks a number

k

from the set

\{1,2,\ldots,187\}

, and Bob will tell Alice the value of

f(k)

. Find the smallest positive integer

N

so that Alice always knows for sure the parity of

f(0)

within

N

turns.
Proposed by YaWNeeT

Problem Statement