Contests & Programs
AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
3
M
G
BBookmark
VNew Topic
kLocked
Contests & Programs
AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
3
M
G
BBookmark
VNew Topic
kLocked
No tags match your search
Mmodular arithmetic
AMC
AIME
AMC 10
geometry
USA(J)MO
AMC 12
USAMO
AIME I
AMC 10 A
USAJMO
AMC 8
poll
MATHCOUNTS
AMC 10 B
number theory
probability
summer program
trigonometry
algebra
AIME II
AMC 12 A
function
AMC 12 B
email
calculus
ARML
inequalities
analytic geometry
3D geometry
ratio
polynomial
AwesomeMath
search
AoPS Books
college
HMMT
USAMTS
Alcumus
quadratics
PROMYS
geometric transformation
Mathcamp
LaTeX
rectangle
logarithms
modular arithmetic
complex numbers
Ross Mathematics Program
contests
AMC10
No tags match your search
MG
Topic
First Poster
Last Poster
Inequality
Sappat 10
N
an hour ago
by iamnotgentle
Let
be real numbers such that
. Prove that



10 replies

ISI UGB 2025 P4
SomeonecoolLovesMaths 9
N
an hour ago
by nyacide
Source: ISI UGB 2025 P4
Let
be the unit circle in the complex plane. Let
be the map given by
. We define
and
for
. The smallest positive integer
such that
is called the period of
. Determine the total number of points in
of period
.
(Hint :
)











(Hint :

9 replies
Self-evident inequality trick
Lukaluce 9
N
an hour ago
by sqing
Source: 2025 Junior Macedonian Mathematical Olympiad P4
Let
, and
be positive real numbers, such that
. Prove the inequality
When does the equality hold?



![\[\frac{x^3}{2 + x} + \frac{y^3}{2 + y} + \frac{z^3}{2 + z} \ge 1.\]](http://latex.artofproblemsolving.com/b/e/5/be5819a67c3cd78f2dea35fdccf48688c720ce3c.png)
9 replies
Prove n is square-free given divisibility condition
CatalanThinker 1
N
an hour ago
by CatalanThinker
Source: 1995 Indian Mathematical Olympiad
Let
be a positive integer such that
divides the sum
Prove that
is square-free.


![\[
1 + \sum_{i=1}^{n-1} i^{n-1}.
\]](http://latex.artofproblemsolving.com/e/2/d/e2daf7800da3f984cd761ed1fecf10083444db25.png)

1 reply
What is thiss
EeEeRUT 5
N
2 hours ago
by MathLuis
Source: Thailand MO 2025 P6
Find all function
,such that the inequality
holds for all positive reals
and for every positive real
, there exist positive reals
, such that the equality holds.





5 replies

Thailand geometry
EeEeRUT 4
N
2 hours ago
by MathLuis
Source: Thailand MO 2025 P7
Let
be a triangle with
. The tangent to the circumcircle of
at
intersects
at
. The angle bisector of
intersect
at
. Suppose that the perpendicular bisector of
intersect
at
, respectively. Show that













4 replies
JBMO Shortlist 2021 G2
Lukaluce 10
N
2 hours ago
by Adventure1000
Source: JBMO Shortlist 2021
Let
be an interior point of the isosceles triangle
with
. If
prove that
.
Proposed by Mehmet Akif Yıldız, Turkey





Proposed by Mehmet Akif Yıldız, Turkey
10 replies

Thailand MO 2025 P3
Kaimiaku 5
N
2 hours ago
by MathLuis
Let
be positive real numbers such that
. Prove that



5 replies
Simple inequality
sqing 7
N
2 hours ago
by sqing
Source: 2016 China Sichuan High School Mathematics Competition ,Q14
Let
are positive real numbers .Show that


7 replies
