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

Revision as of 17:58, 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

$\frac{(5m)!(5n)!}{m!n!(3m+n)!(3n+m)!}$

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.

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 {{USAMO box|year=1975|before=First Question|num-a=2}}
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 [[Category:Olympiad Number Theory Problems]]

1975 USAMO (Problems • Resources)
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