Difference between revisions of "2006 USAMO Problems/Problem 1"
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* [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=490569#p490569 Discussion on AoPS/MathLinks] | * [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=490569#p490569 Discussion on AoPS/MathLinks] | ||
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+ | [[Category:Olympiad Number Theory Problems]] |
Revision as of 20:24, 1 September 2006
Problem
Let be a prime number and let
be an integer with
. Prove that there exist integers
and
with
and
if and only if is not a divisor of
.
Note: For a real number, let
denote the greatest integer less than or equal to
, and let
denote the fractional part of
.
Solution
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