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Show that there exists a positive multiple of 1996 whose sum of digits is 1996.
in Mathematics by Platinum (142,760 points) | 67 views

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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
\[
1996 \cdot 100010001000 \ldots 1000200002
\]
by Platinum (142,760 points)

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