Complicated FE
by XAN4, Apr 23, 2025, 11:53 AM
Find all solutions for the functional equation 
, in which 
: 
Note: the solution is actually quite obvious -
, but the proof is important.
Note 2: it is likely that the result can be generalized into a more advanced questions, potentially involving more bash.
, in which 
: 
Note: the solution is actually quite obvious -
, but the proof is important.Note 2: it is likely that the result can be generalized into a more advanced questions, potentially involving more bash.
is a cyclic quadrilateral with 
.
and 
be the feet of perpendiculars from 
and 
to 
respectively. Prove that 
.
on the whiteboard. In each move, she selects two distinct numbers, 
and 
,
.
,
,
,
is a prime.
,
is a perfect square.
,
is fantabulous, then all the elements are fantabulous. Does it follow that the number 
is fantabulous?
and 
be on segment 
of an acute triangle 
such that 
and 
.
and 
be the points on 
and 
,
and 
.
and 
is on the circumference of triangle 
represent the circumcircle of triangle 
.
intersect 
.
and 
respectively. Let 
and 
meet at 
.
.
is a kite with 
,
.
bisects 
shows that 
are collinear.
and 
consisting of a prime number 
and two positive integers 
such that 
and 
are both powers of 
be integers. Suppose that for each 
there exists an integer 
such that 
is divisible by 
for some integer 
March 2018
February 2018