Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

1995 USAMO Problems/Problem 4

Revision as of 06:42, 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>...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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 $n$.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1995_USAMO_Problems/Problem_4&oldid=57190"