Difference between revisions of "1999 USAMO Problems/Problem 3"
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Revision as of 13:35, 4 July 2013
Problem
Let 
be a prime and let 
be integers not divisible by 
, such that
![\[\left\{ \dfrac{ra}{p} \right\} + \left\{ \dfrac{rb}{p} \right\} + \left\{ \dfrac{rc}{p} \right\} + \left\{ \dfrac{rd}{p} \right\} = 2\]](http://latex.artofproblemsolving.com/5/c/1/5c153c8aae6d134a748186f7f7201fa0d68aad5a.png)
for any integer 
not divisible by . Prove that at least two of the numbers 
, 
, 
, 
, 
, 
are divisible by .
(Note: 
denotes the fractional part of 
.)
Solution
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See Also
| 1999 USAMO (Problems • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAMO Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
