Maths Olympiad Prep

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Problem 1491

National Olympiad, first round
Number theory Difficulty 6.0 Prove it KöMaL problem A · Hungary · 2022

Sets XZ+X\subset \mathbb{Z}^{+} and YZ+Y\subset \mathbb{Z}^{+} are called comradely, if every positive integer nn can be written as n=xyn=xy for some xXx\in X and yYy\in Y. Let X(n)X(n) and Y(n)Y(n) denote the number of elements of XX and YY, respectively, among the first nn positive integers.

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