No tags match your search
Mfloor function
geometry
algebra
number theory
trigonometry
inequalities
function
polynomial
probability
combinatorics
calculus
analytic geometry
3D geometry
quadratics
AMC
ratio
AIME
modular arithmetic
logarithms
LaTeX
complex numbers
rectangle
conics
circumcircle
geometric transformation
induction
integration
floor function
system of equations
counting
perimeter
rotation
trig identities
vector
trapezoid
search
graphing lines
angle bisector
prime numbers
slope
parallelogram
AMC 10
symmetry
relatively prime
parabola
Diophantine equation
Vieta
angles
factorial
Inequality
domain
No tags match your search
MG
Topic
First Poster
Last Poster
Hojoo Lee problem 73
Leon 25
N
23 minutes ago
by sqing
Source: Belarus 1998
Let
,
,
be real positive numbers. Show that



![\[\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\geq \frac{a+b}{b+c}+\frac{b+c}{a+b}+1\]](http://latex.artofproblemsolving.com/0/9/5/0959464bbb9b821a11df292f9e6addded7326371.png)
25 replies


Almost Squarefree Integers
oVlad 3
N
30 minutes ago
by Primeniyazidayi
Source: Romania Junior TST 2025 Day 1 P1
A positive integer
is almost squarefree if there exists a prime number
such that
and
is squarefree. Prove that for any almost squarefree positive integer
the ratio
is an integer.






3 replies



Math camp combi
ErTeeEs06 3
N
31 minutes ago
by genius_007
Source: BxMO 2025 P2
Let
be a natural number. At a mathematical olympiad training camp the same
courses are organised every day. Each student takes exactly one of the
courses each day. At the end of the camp, every student has takes each course exactly once, and any two students took the same course on at least one day, but took different courses on at least one other day. What is, in terms of
, the largest possible number of students at the camp?




3 replies
Benelux fe
ErTeeEs06 10
N
40 minutes ago
by genius_007
Source: BxMO 2025 P1
Does there exist a function
such that
for all
?



10 replies
IMO Shortlist Problems
ABCD1728 0
an hour ago
Source: IMO official website
Where can I get the official solution for ISL before 2005? The official website only has solutions after 2006. Thanks :)
0 replies
Geometric inequality in quadrilateral
BBNoDollar 0
an hour ago
Source: Romanian Mathematical Gazette 2025
Let ABCD be a convex quadrilateral with angles BAD and BCD obtuse, and let the points E, F ∈ BD, such that AE ⊥ BD and CF ⊥ BD.
Prove that 1/(AE*CF) ≥ 1/(AB*BC) + 1/(AD*CD) .
Prove that 1/(AE*CF) ≥ 1/(AB*BC) + 1/(AD*CD) .
0 replies
A coincidence about triangles with common incenter
flower417477 2
N
an hour ago
by flower417477




2 replies
Function equation
LeDuonggg 5
N
2 hours ago
by luutrongphuc
Find all functions
, such that for all
:


![\[ f(x+f(y))=\dfrac{f(x)}{1+f(xy)}\]](http://latex.artofproblemsolving.com/1/4/1/1418fad9fd00b31c38bfbc5657e2a322d66ef450.png)
5 replies


Consecutive sum of integers sum up to 2020
NicoN9 2
N
2 hours ago
by NicoN9
Source: Japan Junior MO Preliminary 2020 P2
Let
and
be positive integers. Suppose that the sum of integers between
and
, including
and
, are equal to
.
All among those pairs
, find the pair such that
achieves the minimum.







All among those pairs


2 replies
Range of a^3+b^3-3c
Kunihiko_Chikaya 1
N
2 hours ago
by Mathzeus1024
Let
be real numbers such that
and

Find the range of
Proposed by Kunihiko Chikaya/September 23, 2020



Find the range of

Proposed by Kunihiko Chikaya/September 23, 2020
1 reply

