Difference between revisions of "1975 USAMO Problems/Problem 1"

m (See also)
Line 14: Line 14:
{{USAMO box|year=1975|before=First Question|num-a=2}}
{{USAMO box|year=1975|before=First Question|num-a=2}}
{{MAA Notice}}
[[Category:Olympiad Number Theory Problems]]
[[Category:Olympiad Number Theory Problems]]

Revision as of 18:58, 3 July 2013


(a) Prove that

$[5x]+[5y]\ge [3x+y]+[3y+x]$,

where $x,y\ge 0$ and $[u]$ denotes the greatest integer $\le u$ (e.g., $[\sqrt{2}]=1$).

(b) Using (a) or otherwise, prove that


is integral for all positive integral $m$ and $n$.


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

See Also

1975 USAMO (ProblemsResources)
Preceded by
First Question
Followed by
Problem 2
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

Invalid username
Login to AoPS