by truongphatt2668, May 15, 2025, 1:05 PM ![$P(x) \in \mathbb{R}[x]$](http://latex.artofproblemsolving.com/4/5/3/453a624c3b002c1b0e78e0023b24dd22ddd03557.png)
such that:
with 
is an 
th prime and 
is an arbitrary positive integer.by Rayanelba, May 15, 2025, 12:37 PM 
that verify the following equation :
by steven_zhang123, May 14, 2025, 11:09 PM 
, 
. The internal angle bisector of 
and the external angle bisector of intersect the ray 
at points 
and 
, respectively. Given that 
, prove that 
.by AlperenINAN, May 11, 2025, 7:15 PM 
be a cyclic quadrilateral and let the intersection point of lines 
and 
be . Let the points 
and 
be arbitrary points on sides and respectively, which satisfy the conditions
Prove that 
.by sevket12, Feb 8, 2025, 12:39 PM 
such that the number![\[
\frac{3 + \sqrt{4n + 9}}{2}
\]](http://latex.artofproblemsolving.com/f/2/f/f2f09c19d46025866c5116d6909b3e9ab5e2ac66.png)
is the sixth smallest positive divisor of .by BartSimpsons, May 14, 2017, 3:20 PM 
be a triangle with 
. Let be the intersection point of the internal bisector of angle 
and the circumcircle of . Let 
be the intersection point of the perpendicular bisector of 
with the external bisector of angle 
. Prove that the midpoint of the segment lies on the circumcircle of triangle 
.by YanYau, Apr 8, 2016, 9:16 AM 
be the diameter of semicircle 
. Circle 
is internally tangent to and tangent to at 
. Let 
be a point on and 
a point on such that 
and is tangent to . Prove that bisects 
by sartt, May 3, 2011, 11:23 AM 
be the midpoint of arc of the circumcircle of triangle , let 
be the midpoint of and let 
be the incentres of triangles 
and 
. Prove that points 
lie on a circle.by canada, Jul 7, 2010, 4:32 PM 
such that for all 
the following equality holds ![\[
f(\left\lfloor x\right\rfloor y)=f(x)\left\lfloor f(y)\right\rfloor \]](http://latex.artofproblemsolving.com/f/3/a/f3ac860e90d671f9fb592a6bd55c102a3000daec.png)
where 
is greatest integer not greater than 
Stay insane,Coz it's your will, labour and pain,which takes you to the top of the mountain.
September 2017
February 2017
September 2016
July 2016
April 2016
March 2016
December 2015
November 2015
August 2015
April 2015
March 2015
February 2015
January 2015
October 2014
September 2014
August 2014
July 2014