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Values of n-f(n)

Source: 2023 Turkey TST D1 P3

March 29, 2023
number theoryequation

Problem Statement

For all n>1n>1, let f(n)f(n) be the biggest divisor of nn except itself. Does there exists a positive integer kk such that the equality nāˆ’f(n)=kn-f(n)=k has exactly 20232023 solutions?
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