Difference between revisions of "1997 USAMO Problems"
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[http://www.artofproblemsolving.com/Wiki/index.php/Problem_1 Solution] | [http://www.artofproblemsolving.com/Wiki/index.php/Problem_1 Solution] | ||
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+ | == Problem 2 == | ||
+ | Let <math>ABC</math> be a triangle, and draw isosceles triangles <math>BCD, CAE, ABF</math> externally to <math>ABC</math>, with <math>BC, CA, AB</math> as their respective bases. |
Revision as of 21:04, 30 June 2011
Problem 1
Let be the prime numbers listed in increasing order, and let
be a real number between
and
. For positive integer
, define
where denotes the fractional part of
. (The fractional part of
is given by
where
is the greatest integer less than or equal to
.) Find, with proof, all
satisfying
for which the sequence
eventually becomes
.
Problem 2
Let be a triangle, and draw isosceles triangles
externally to
, with
as their respective bases.