1975 USAMO Problems/Problem 1
Problem
(a) Prove that
![$[5x]+[5y]\ge [3x+y]+[3y+x]$](http://latex.artofproblemsolving.com/f/3/5/f35b4df2174c9e93d13d91ef893d3c1743e22e01.png)
where and
denotes the greatest integer
(e.g.,
).
(b) Using (a) or otherwise, prove that
![$\frac{(5m)!(5n)!}{m!n!(3m+n)!(3n+m)!}$](http://latex.artofproblemsolving.com/8/a/d/8adf3172b9cbf506283e6114ccb395d9c4901dcf.png)
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 |