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S(ab) = S(bc) = S(ca) = N

Source: 2010 Peru Iberoamerican TST problem 2

May 9, 2023
number theory

Problem Statement

For each positive integer kk, let S(k)S(k) be the sum of the digits of kk in the decimal system. Find all positive integers N for which there exist positive integers aa,bb,cc, coprime two by two, such that: S(ab)=S(bc)=S(ca)=NS(ab) = S(bc) = S(ca) = N.
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