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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.
,
.
such that 
,
.
satisfying the system of equations:
,
.
.
is given by 
.
without satisfying 
.
Y by
Let 
be a triangle and let 
and 
be points on the line 
such that 
, 
and 
are altitude, angle bisector and median of the triangle, respectively. It is known that ![$$\frac{[AMP]}{[ABC]}=\frac14 \,\,\,, \,\,\, \frac{[ANP]}{[ABC]}= 1 - \frac{\sqrt3}{2}.$$](//latex.artofproblemsolving.com/b/7/0/b70b9e0531d858e422d651d4066d64b65e1861ce.png)
Determine the angles of triangle .
Note:![$[P]$](//latex.artofproblemsolving.com/8/2/c/82c8af2036036acc93984fa2d3e7fac5cb926624.png)
denotes the area of the polygon .
be a triangle and let 
and 
be points on the line 
such that 
, 
and 
are altitude, angle bisector and median of the triangle, respectively. It is known that ![$$\frac{[AMP]}{[ABC]}=\frac14 \,\,\,, \,\,\, \frac{[ANP]}{[ABC]}= 1 - \frac{\sqrt3}{2}.$$](http://latex.artofproblemsolving.com/b/7/0/b70b9e0531d858e422d651d4066d64b65e1861ce.png)
Determine the angles of triangle .Note:
![$[P]$](http://latex.artofproblemsolving.com/8/2/c/82c8af2036036acc93984fa2d3e7fac5cb926624.png)
denotes the area of the polygon .This post has been edited 1 time. Last edited by parmenides51, Nov 10, 2021, 12:25 AM
