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Aproximation of a polynomial !

Source: India TST 2001 Day 5 Problem 3

January 31, 2015
algebrapolynomialinequalitiesinductionalgebra unsolved

Problem Statement

Let P(x)P(x) be a polynomial of degree nn with real coefficients and let a≥3a\geq 3. Prove that max⁡0≤j≤n+1∣aj−P(j)∣≥1\max_{0\leq j \leq n+1}\left | a^j-P(j) \right |\geq 1
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