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geometry (In the World of Mathematics) (>>) Greek Aops Index Greek Aops Index - Άλγεβρα Greek Aops Index - Ανισότητες Greek Aops Index - Γεωμετρία Greek Aops Index - Θεωρία Αριθμών Greek Aops Index - Συνδυαστική
such that 
is a square.
such that there is a polynomial 
with integer coefficients for which 
and where 
is a prime number .
letters. A sequence of letters is a word, if there are no two equal letters between two other equal letters. Find the number of words of the maximum length.
defined on the positive reals such that 
for all 
.
such that 
is a perfect square, i.e., the square of an integer.
, without repetition. Find the largest multiple of 
. Justify your answer.
such that 
, for all 
.
satisfying the system of equations:
, compute the ratio 
. Prove that sum of these ratios is at least 
.
is given by 
.
without satisfying 
.
and 
be the altitudes of the triangle 
. Prove that 
if and only if 
.
and 
,
.
,
as desired. Now we prove the "only if." We'll show it's not possible to have 
.
.
,
,