[/quote]
,
be the largest real solution to the equation ![\[\frac{3}{x-3}+\frac{5}{x-5}+\frac{17}{x-17}+\frac{19}{x-19}= x^2-11x-4.\]](http://latex.artofproblemsolving.com/e/8/7/e87fdc9fe63d29a46e57dfb92c2d0448441b4b55.png)
There are positive integers 
such that 
.
.
where 
is a positive integer and 
is a prime.(Don't get mad at me,I've used the search function and did not see a correct and complete solution anywhere.)
such that 
divides 
for all positive integers 
and 
with 
.
,
such that 
is a perfect square? (Here 
denotes the integer part of the real number 
?
be an acute triangle with 
,
be the intouch triangle with 
,
,
,
be the intersecttion of the perpendicular from 
to 
with 
,
.
and 
are concylic
the set 
can be partitioned into 
,
,
.
and that 
.
and 
be the midpoints of sides 
,
and 
be the feet of the altitudes from 
and 
in 
,
be the intersection of line 
with the tangent line to 
.
be the intersection point, other than 
.
be the intersection of lines 
and 
.
with centre 
passes through 
respectively. Let 
,
is equidistant from 
is a cyclic quadrilateral inscribed in a circle of radius one unit. If 
,
,
,
,
satisfy 
and 
.
of 
such that 
.
Y by TheOneYouWant, Tawan, skys, Adventure10, Mango247
Let the nervous waiting commence!
No talking about about how to solve the problems.
I've done ~4, and fully locked down 2.
How is everyone else doing?
No talking about about how to solve the problems.
I've done ~4, and fully locked down 2.
How is everyone else doing?
This post has been edited 1 time. Last edited by xPythagoras, Feb 15, 2016, 10:10 PM
Reason: No one seemed to like the other 'rules'
Reason: No one seemed to like the other 'rules'
skills
