1995 USAMO Problems/Problem 4

Problem

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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1995 USAMO (Problems • Resources)
Preceded by Problem 3	Followed by Problem 5
1 • 2 • 3 • 4 • 5
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