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F.E....can you solve it?
Jackson0423 0
Find all functions 
such that
![\[
f\left(\frac{x^2 - f(x)}{f(x) - 1}\right) = x
\]](//latex.artofproblemsolving.com/8/0/0/8009a4709ffd6708023d67db2b544e605d1fbe68.png)
for all real numbers 
satisfying 
.
such that![\[
f\left(\frac{x^2 - f(x)}{f(x) - 1}\right) = x
\]](http://latex.artofproblemsolving.com/8/0/0/8009a4709ffd6708023d67db2b544e605d1fbe68.png)
for all real numbers 
satisfying 
.
0 replies
Functional equation
Math-wiz 25
N
by Adywastaken
Source: IMOC SL A1
Find all functions 
such that for all 
,
such that for all 
,
25 replies
Nice numer theory
GeoArt 5
N
by Primeniyazidayi
is a prime number, 
are natural numbers (
). It is known that 
. Prove that 
.
5 replies
Prove XBY equal to angle C
nataliaonline75 2
N
by starchan
Let 
be the midpoint of 
on triangle 
. Point 
lies on segment 
such that 
and 
on line 
such that 
. Prove that 
.
be the midpoint of 
on triangle 
. Point 
lies on segment 
such that 
and 
on line 
such that 
. Prove that 
.
2 replies
Unique number to make a square of a rational
Zavyk09 2
N
by Zavyk09
Source: Homework
Find all positive integers 
there exists a unique positive integers 
such that 
is a square of a rational number.
there exists a unique positive integers 
such that 
is a square of a rational number.
2 replies
Classical NT using modular arithmetic
electrovector 7
N
by Blackbeam999
Source: 2022 Turkey TST P1 Day 1 + 2023 Dutch BxMO TST, Problem 5
Find all pairs of prime numbers 
for which
![\[2^p = 2^{q-2} + q!.\]](//latex.artofproblemsolving.com/8/8/2/88270dc4aa4a54cc8b2e525b7d9d940c300e49ac.png)
for which![\[2^p = 2^{q-2} + q!.\]](http://latex.artofproblemsolving.com/8/8/2/88270dc4aa4a54cc8b2e525b7d9d940c300e49ac.png)
7 replies
Inequality
lgx57 9
N
by lgx57
Source: Own
. Prove that
(I don't know whether the equality holds)
9 replies
are positive numbers, then prove that
Prove that
Where 
we can find one pair of a boy and a girl
orl 18
N
by bin_sherlo
Source: Vietnam TST 2001 for the 42th IMO, problem 3
Some club has 42 members. It’s known that among 31 arbitrary club members, we can find one pair of a boy and a girl that they know each other. Show that from club members we can choose 12 pairs of knowing each other boys and girls.
18 replies
