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| f(x) - P(x)| <= c * x^{1998}

Source: Vietnam TST 1998 for the 39th IMO, problem 1

June 26, 2005

functionalgebrapolynomiallimitalgebra unsolved

Problem Statement

Let

f(x)

be a real function such that for each positive real

c

there exist a polynomial

P(x)

(maybe dependent on

c

) such that

| f(x) - P(x)| \leq c \cdot x^{1998}

for all real

x

. Prove that

f

is a real polynomial.