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

m
Line 15: Line 15:
 
== See Also ==
 
== See Also ==
 
{{USAMO box|year=1978|num-b=2|num-a=4}}
 
{{USAMO box|year=1978|num-b=2|num-a=4}}
 +
{{MAA Notice}}
  
 
[[Category:Olympiad Number Theory Problems]]
 
[[Category:Olympiad Number Theory Problems]]

Revision as of 19:06, 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

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See Also

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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png