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1995 USAMO Problems/Problem 4

Revision as of 07:42, 4 October 2013 by Euler brick (talk | contribs) (Created page with "Suppose <math>q_1,q_2,...</math> is an infinite sequence of integers satisfying the following two conditions: (a) <math>m - n </math> divides <math>q_m - q_n</math> for <math>m>...")
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Suppose $q_1,q_2,...$ is an infinite sequence of integers satisfying the following two conditions:

(a) $m - n$ divides $q_m - q_n$ for $m>n \geq 0$

(b) There is a polynomial $P$ such that $|q_n|<P(n)$ for all $n$.

Prove that there is a polynomial $Q$ such that $q_n = Q(n)$ for each $n$.

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