[/quote]
,
.
that satisfies![\[ f(x+yf(x))f(y)=f(x)(1+yf(y+1)) \]](http://latex.artofproblemsolving.com/f/7/a/f7a138fd2dc76f034525491a10f62f1e83de294d.png)
for all 
.
,
be positive integers such that 
is a multiple of 
for all positive integers 
.
with 
is called historic if 
.
satisfying 
for all pairs of positive reals 
and 
.
denotes the set of all positive reals.
be positive real numbers such that : 
. Prove that : 
L
be positive reals numbers such that 
.
satisfying: 
,
and the function 
defined by![\[f(n)=\left\lfloor \frac{an+b}{cn+d}\right\rfloor\text{ for all } n\in\mathbb{Z}_{\ge 0}.\]](http://latex.artofproblemsolving.com/8/f/b/8fb372df4b44c3d7c0690b310b12c684134fee74.png)
Prove that the following are equivalent:
is surjective;
,
and 
.
be on sides 
and 
respectively in 
such that 
.
be the circumcenter of 
and let 
.
,
is the set of real numbers, such that
be the n-th prime number in increasing order for 
.
satisfying 
for all 
Y by Adventure10
On a board are drawn the points 
. Yetti constructs the points 
in the following way: 
is the symmetric of 
with respect to 
, 
is the symmetric of wrt 
, 
is the symmetric of wrt 
and 
is the symmetric of wrt .
Suppose that Armpist erases the points. Can Yetti rebuild them?
Note. Any similarity to real persons is purely accidental.
. Yetti constructs the points 
in the following way: 
is the symmetric of 
with respect to 
, 
is the symmetric of wrt 
, 
is the symmetric of wrt 
and 
is the symmetric of wrt .Suppose that Armpist erases the points
. Can Yetti rebuild them?
Note. Any similarity to real persons is purely accidental.
This post has been edited 1 time. Last edited by perfect_radio, Apr 22, 2006, 10:14 PM
?
is the symmetric of 
.
.
and 
be the points on 
and 
such that 
.
such that 
.
in function of 
