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new sumbol, n'

Source: Flanders Math Olympiad 2017 p4

December 24, 2022
number theoryalgebra

Problem Statement

For every natural number nn we define the derived number n′n' as follows: ∙\bullet 0′=1′=00' = 1' = 0 ∙\bullet if nn is prime, then n′=1n' = 1 ∙\bullet if n=a⋅bn = a \cdot b, then n′=a′b+ab′n' = a' b + a b' . For example: 15′=3′5+35′=1⋅5+3⋅1=815' = 3' 5 + 3 5' = 1\cdot 5 + 3\cdot 1 = 8. Determine all natural numbers nn for which n=n′n = n'.
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