MathDB

Ali and Naqi are playing a game. At first, they have Polynomial

P(x) = 1+x^{1398}

. Naqi starts. In each turn one can choice natural number

k \in [0,1398]

in his trun, and add

x^k

to the polynomial. For example after 2 moves

P

can be :

P(x) = x^{1398} + x^{300} + x^{100} +1

. If after Ali's turn, there exist

t \in R

such that

P(t)<0

then Ali loses the game. Prove that Ali can play forever somehow he never loses the game!

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