[/quote]
,
,
be positive integers such that 
.
is a sequence of integers satisfying 
,
,
,
Prove that there exists 
such that 
and 
and 
that always satisfy the following condition:
such that 
,
such that 
be an equilateral triangle, and 
is a point on its incircle. Let 
be the circle tangent to 
passing through 
.
be the circle tangent to 
passing through 
,
be the circle tangent to 
passing through 
.
with degree 
,
with product 
,
Suppose there exist positive reals 
with product 
Is it possible that the values 
satisfying 
Prove that 
Proposed by Phan Ngoc Chau
is called \textit{good}, if 
are non-negative integers, and 
is either 
or 
.
such that 
Suppose Ivan starts with the least possible number of ones to obtain 
after some steps, determine the minimum number of steps he will need in order to do so.
,
positive (not neccesarily distinct) real numbers 
,
.
where 
is a fixed positive real number, with exactly 
,
,
and 
are considered different ways to fill the asterisks, and the chosen terms need not be distinct, for example 
.
and 
.
,
,
and 
intersect the circumcircle of 
,
and 
respectively. Let 
,
be diameters in the circumcircles of triangles 
and 
respectively.
.
be the set of real numbers. Find all functions 
where there exist a real constant 
such that 
holds for all reals 
,
,
that satisfy 
.
where 
.
Y by Adventure10, Mango247
Hello peoples:
I need help on a problem. If you know the solution, could you please post it, and tell me how to do it? Here is the problem:
"The product (66)(9)(22)(39) has a prime factorization of the form (2A)(3B)(11C)(13D). What is the value of ac-bd? "
{Note: 2a actually represents "2 to the power of a", same goes for 3b,11c, & 13D}
PLEASE HELP ME!
: 
I need help on a problem. If you know the solution, could you please post it, and tell me how to do it? Here is the problem:
"The product (66)(9)(22)(39) has a prime factorization of the form (2A)(3B)(11C)(13D). What is the value of ac-bd? "
{Note: 2a actually represents "2 to the power of a", same goes for 3b,11c, & 13D}
PLEASE HELP ME!
: 
