[/quote]
,
and 
be 2 distinct positive integers.
be in an integer. Prove why ?
is given. It turns out that for every positive integer number 
,
and 
are positive, they have the same number of divisors. Is it necessarily true that 
?
with 
as its incenter. Let 
be the intersection of 
and 
and define 
in a similar way. Furthermore, let 
.
,
are concyclic.
positive integers. Product of any one of them with sum of remaining numbers increased by 
is divisible with sum of all 
![$P \in \mathbb R[x,y]$](http://latex.artofproblemsolving.com/8/a/0/8a0576299e976c51607959fb68c7c742b2a49c6a.png)
with ![$P \not\in \mathbb R[x] \cup \mathbb R[y]$](http://latex.artofproblemsolving.com/a/f/7/af71ba8c643d5bd8a2928fa6714ccd91713bd641.png)
and 
homeomorphismes of 
,
is an homoemorphisme too.
is inscribed in a circle centered at 
,
.
be the second intersection point of the circumcircles of the triangles 
and 
.
,
and 
are the circumcenters of the triangles 
are concyclic.
where 
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.)
![\[
2^a + 3^b + 1 = 6^c
\]](http://latex.artofproblemsolving.com/1/9/e/19eb5efa2ccdf54cd277339f8d3b99f75168779d.png)
is inscribed in circle 
.
and 
and 
be the midpoints of sides 
and 
,
and 
meet 
and 
,
and 
meet at 
.
satisfying both of the following properties:
.
.
with maximums 
and 
.
,
can be expressed as 
where 
and 
for each nonnegative integer 
.
is the greatest integer less than or equal to 
,
and 
.
Let 
.
Let 
.
Let 
.
Y by
How many ways are there to color the 
regions of a three-set Venn Diagram with 
colors such that each color is used at least once? Two colorings are considered the same if one can be reached from the other by rotation and reflection.
Non ai way btw pls
regions of a three-set Venn Diagram with 
colors such that each color is used at least once? Two colorings are considered the same if one can be reached from the other by rotation and reflection.Non ai way btw pls
This post has been edited 2 times. Last edited by Rice_Farmer, Today at 3:35 AM
