1995 IMO Problems/Problem 6
Problem
Let be an odd prime number. How many -element subsets of are there, the sum of whose elements is divisible by ?
Solution 1 (Partition)
Let be the generating function
We apply the roots of unity filter on to get
We call this function on , . Note that
Then, we apply the roots of unity filter on to get
But, we need to subtract because it counts the empty set and the set with size . This gives us
Solution from this discussion: https://artofproblemsolving.com/community/c6t302107f6h15112_sum_of_whose_elements_is_divisible_by_p.
See Also
1995 IMO (Problems) • Resources | ||
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