IMO 1979 LL HUN40
A polynomial P(x) has degree at most 2k, where k = 0, 1,
IMO 1979 LL HUN40
Origin: HUN
Problem
A polynomial P(x) has degree at most 2k, where k = 0, 1, 2, . . . . Given that for an integer i, the inequality −k \leqi \leqk implies |P(i)| \leq1, prove that for all real numbers x, with −k \leqx \leqk, the following inequality holds: |P(x)| < (2k + 1) 2k k .