Difference between revisions of "1997 IMO Problems/Problem 6"
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Revision as of 16:22, 6 October 2023
Problem
For each positive integer , let denote the number of ways of representing as a sum of powers of with nonnegative integer exponents. Representations which differ only in the ordering of their summands are considered to be the same. For instance, , because the number 4 can be represented in the following four ways:
Prove that, for any integer ,
.
Solution
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