MathDB
Polynomial

Source: 17-th Iranian Mathematical Olympiad 1999/2000; 6th German TST 2005, problem 2

October 26, 2003
algebrapolynomialfunctionIranpower of 2

Problem Statement

For any positive integer n n, prove that there exists a polynomial P P of degree n n such that all coeffients of this polynomial P P are integers, and such that the numbers P(0) P\left(0\right), P(1) P\left(1\right), P(2) P\left(2\right), ..., P(n) P\left(n\right) are pairwisely distinct powers of 2 2.
Back to ProblemsView on AoPS