1994 USAMO Problems/Problem 5: Difference between revisions
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==See Also== | ==See Also== | ||
{{USAMO box|year=1994|num-b= | {{USAMO box|year=1994|num-b=4|after=Last Problem}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
[[Category:Olympiad Combinatorics Problems]] | [[Category:Olympiad Combinatorics Problems]] | ||
Revision as of 07:03, 19 July 2016
Problem
Let 
and 
denote the number of elements, the sum, and the product, respectively, of a finite set 
of positive integers. (If is the empty set, 
.) Let 
be a finite set of positive integers. As usual, let 
denote 
. Prove that ![\[\sum_{U \subseteq S} (-1)^{|U|} \binom{m - \sigma(U)}{|S|} = \pi(S)\]](http://latex.artofproblemsolving.com/5/0/e/50ed2758adcf62f11d440689fd8665ae335512b4.png)
for all integers 
.
Solution
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See Also
| 1994 USAMO (Problems • Resources) | ||
| Preceded by Problem 4 |
Followed by Last Problem | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
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