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Show that there exists a positive multiple of 1996 whose sum of digits is 1996.
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We affirm that the number $m=199619961996 \ldots 199639923992$ satisfies the conditions of the statement. Note that $S(m)=25 \cdot 78+2 \cdot 23=1996$. On the other hand, $m$ is divisible by 1996 , since $m$ equals
$1996 \cdot 100010001000 \ldots 1000200002$
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