MathDB

Let

P(x)

be a polynomial such that the following inequalities are satisfied:

P(0) > 0;

P(1) > P(0);

P(2) > 2P(1) \minus{} P(0); P(3) > 3P(2) \minus{} 3P(1) \plus{} P(0); and also for every natural number

n,

P(n\plus{}4) > 4P(n\plus{}3) \minus{} 6P(n\plus{}2)\plus{}4P(n \plus{} 1) \minus{} P(n). Prove that for every positive natural number

n,

P(n)

is positive.

Problem Statement