Difference between revisions of "1978 USAMO Problems/Problem 3"

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== See Also ==
 
== See Also ==
 
{{USAMO box|year=1978|num-b=2|num-a=4}}
 
{{USAMO box|year=1978|num-b=2|num-a=4}}
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{{MAA Notice}}
  
 
[[Category:Olympiad Number Theory Problems]]
 
[[Category:Olympiad Number Theory Problems]]

Revision as of 18:06, 3 July 2013

Problem

An integer $n$ will be called good if we can write

$n=a_1+a_2+\cdots+a_k$,

where $a_1,a_2, \ldots, a_k$ are positive integers (not necessarily distinct) satisfying

$\frac{1}{a_1}+\frac{1}{a_2}+\cdots+\frac{1}{a_k}=1$.

Given the information that the integers 33 through 73 are good, prove that every integer $\ge 33$ is good.

Solution

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See Also

1978 USAMO (ProblemsResources)
Preceded by
Problem 2
Followed by
Problem 4
1 2 3 4 5
All USAMO Problems and Solutions

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