MathDB

Petya and Vasya play the following game. Petya conceives a polynomial

P(x)

having integer coefficients. On each move, Vasya pays him a ruble, and calls an integer

a

of his choice, which has not yet been called by him. Petya has to reply with the number of distinct integer solutions of the equation

P(x)=a

. The game continues until Petya is forced to repeat an answer. What minimal amount of rubles must Vasya pay in order to win?
(Anant Mudgal)
(Translated from [url=http://sasja.shap.homedns.org/Turniry/TG/index.html]here.)

Problem Statement