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Problem 5 of Second round

Source: XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade

September 9, 2022
number theory

Problem Statement

Let aa, bb and cc be given positive integers which are two by two coprime. A positive integer nn is called sozopolian, if it can’t be written as n=bcx+cay+abzn=bcx+cay+abz where xx, yy, zz are also positive integers. Find the number of sozopolian numbers as a function of aa, bb and cc.
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