there exists an 
all of whose digits are odd.
,
,
,
be distinct positive integers, 
.
and 
such that 
does not divide any of the numbers 
,
,
.
Y by Adventure10, Mango247
In triangle 
, angles 
are acute. Point 
is on the side 
such that 
. Let the interior bisectors of 
meet 
at 
, respectively. If 
, prove that is isosceles.
, angles 
are acute. Point 
is on the side 
such that 
. Let the interior bisectors of 
meet 
at 
, respectively. If 
, prove that is isosceles.
then 
.![\[AB^2-BD^2=AC^2-CD^2
\]](http://latex.artofproblemsolving.com/f/3/d/f3d5d4e454f2527d0cefc70a0a01a2d5d43dea6b.png)
![\[\frac{AB^2}{BD^2}-1>\frac{AC^2}{CD^2}-1
\]](http://latex.artofproblemsolving.com/6/9/8/698a04d4271f5a9aac79103b5cd38bcc558fb5f2.png)
![\[\frac{AB}{BD}>\frac{AC}{CD}
\]](http://latex.artofproblemsolving.com/2/d/a/2da63681725f06ceadf262941172018cba391349.png)
![\[\frac{AE}{ED}>\frac{AF}{FD}\implies DF>DE
\]](http://latex.artofproblemsolving.com/3/5/c/35c676a4c6d03678d14f7bc540b2308affd10e32.png)
Thus we have 
,
.
.
.
.
.
.
=
=
.
.
and 
is an increasing function on 
)
.
and 
.
.
![$[0,\dfrac {\pi} {2}]$](http://latex.artofproblemsolving.com/1/a/8/1a8eca21213da2a7790690343dc41e1181722ba7.png)
)
.
.
