[/quote]
,
such that![\[f(x+yf(x))+f(xf(y)-y)=f(x)-f(y)+2xy\]](http://latex.artofproblemsolving.com/e/b/c/ebccae7e765d9fc3c8605e58a7399a70127b39b1.png)
(use in a problem for junior) to practice. Can anyone share to me?
, such that 
Prove that :
equality cases : ?
distinct positive integers such that adding the product of any two of them to 
yields a perfect square?
be a sequence of positive integers with 
,
and![\[a_n = a_{n-1}^{a_{n-1}a_{n-2}}-1\]](http://latex.artofproblemsolving.com/1/b/f/1bf1a88979e7d2b33530de979d66a4e81032953d.png)
for all 
.
is a prime less than 
for some positive integer 
,
such that 
.
be a triangle with circumcircle 
,
.
,
,
with 
,
,
,
intersect at 
and lines 
and 
intersect at 
.
and 
intersect again at 
.
and 
intersect the circumcircle of triangle 
again at 
and 
,
lies on 
.
for which
be an acute angled scalene triangle with circumcircle 
.
and 
be the circumcenter and orthocenter of 
respectively. Let 
and 
be points on segments 
and 
Prove that 
and 
intersect on the circumcircle of 
.
grid with 
the there exist two identical rows (meaning same numbers in the same order).
is called feirense if it is possible to write on a sheet of paper some integers such that every positive divisor of 
side length and with center 
.
is drawn where point 
lies on line 
.
Y by
In the trapezoid 
(
) the bases have lengths 
and 
(
), while the other sides have lengths 
and 
. The diagonals are of lengths 
and 
. It is known that 
.
a) Find the angle between the diagonals of the trapezoid.
b) Prove that
.
c) Prove that
.
(
) the bases have lengths 
and 
(
), while the other sides have lengths 
and 
. The diagonals are of lengths 
and 
. It is known that 
.a) Find the angle between the diagonals of the trapezoid.
b) Prove that
.c) Prove that
.
