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x is divisible by 9 if sums of the digits of x and of 3x are the same

Source: 1993 Swedish Mathematical Competition p1

April 2, 2021
number theorysum of digitsdivisibledivides

Problem Statement

An integer xx has the property that the sums of the digits of xx and of 3x3x are the same. Prove that xx is divisible by 99.
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