1998 APMO Problem #1

Let *F* be the set of all *n*-tuples (*A*_{1}, *A*_{2},
,*A _{n}*) where each

.

Solution #1 by Sasha Schwartz

Of the terms of the form *A*_{1} È
*A*_{2} È
È
*A _{n}* exactly of them dont contain

Therefore, terms contain the integer *m*.

Since this is true for each of the 1998 integers within the range, the total number of elements appearing in each of the terms, which is what was to be computed, is

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