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[[Category:Olympiad Number Theory Problems]] | [[Category:Olympiad Number Theory Problems]] | ||
Revision as of 15:02, 17 September 2012
Problem
(a) Prove that
![$[5x]+[5y]\ge [3x+y]+[3y+x]$](http://latex.artofproblemsolving.com/f/3/5/f35b4df2174c9e93d13d91ef893d3c1743e22e01.png)
,where 
and ![$[u]$](http://latex.artofproblemsolving.com/2/8/0/280a218bdb8d795b8bd3810c97c5b15a6cac3b2a.png)
denotes the greatest integer 
(e.g., ![$[\sqrt{2}]=1$](http://latex.artofproblemsolving.com/6/0/9/6096210e09bfe83fe866eebcae8b65febbf1a331.png)
).
(b) Using (a) or otherwise, prove that
is integral for all positive integral 
and 
.
Solution
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See Also
| 1975 USAMO (Problems • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
