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Prove that there exists a polynomial

P(x)

with real coefficients and degree greater than 1 such that both of the following conditions are true

\cdot

P(a)+P(b)+P(c)\ge 2021

holds for all nonnegative real numbers

a,b,c

such that

a+b+c=3

\cdot

There are infinitely many triples

(a,b,c)

of nonnegative real numbers such that

a+b+c=3

and

P(a)+P(b)+P(c)= 2021

P5