Difference between revisions of "1999 USAMO Problems/Problem 3"
(Created page with "== Problem == Let <math>p > 2</math> be a prime and let <math>a,b,c,d</math> be integers not divisible by <math>p</math>, such that <cmath> \left\{ \dfrac{ra}{p} \right\} + \left...") |
|||
| Line 12: | Line 12: | ||
[[Category:Olympiad Number Theory Problems]] | [[Category:Olympiad Number Theory Problems]] | ||
| + | {{MAA Notice}} | ||
Revision as of 12:35, 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
This problem needs a solution. If you have a solution for it, please help us out by adding it.
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. 
