College Math
Topics in undergraduate and graduate studies
Topics in undergraduate and graduate studies
3
M
G
BBookmark
VNew Topic
kLocked
College Math
Topics in undergraduate and graduate studies
Topics in undergraduate and graduate studies
3
M
G
BBookmark
VNew Topic
kLocked
No tags match your search
Minduction
calculus
real analysis
linear algebra
superior algebra
complex analysis
advanced fields
probability and stats
number theory
topology
Putnam
college contests
articles
function
integration
calculus computations
real analysis unsolved
limit
algebra
trigonometry
matrix
logarithms
derivative
superior algebra unsolved
polynomial
abstract algebra
geometry
inequalities
vector
group theory
linear algebra unsolved
probability
advanced fields unsolved
analytic geometry
domain
induction
LaTeX
Ring Theory
3D geometry
complex analysis unsolved
complex numbers
Functional Analysis
geometric transformation
superior algebra solved
real analysis theorems
search
parameterization
quadratics
real analysis solved
limits
ratio
No tags match your search
MG
Topic
First Poster
Last Poster
Alice and Bob play, 8x8 table, white red black, minimum n for victory
parmenides51 14
N
an hour ago
by Ilikeminecraft
Source: JBMO Shortlist 2018 C3
The cells of a
table are initially white. Alice and Bob play a game. First Alice paints
of the fields in red. Then Bob chooses
rows and
columns from the table and paints all fields in them in black. Alice wins if there is at least one red field left. Find the least value of
such that Alice can win the game no matter how Bob plays.





14 replies
GEOMETRY GEOMETRY GEOMETRY
Kagebaka 71
N
an hour ago
by bin_sherlo
Source: IMO 2021/3
Let
be an interior point of the acute triangle
with
so that
The point
on the segment
satisfies
the point
on the segment
satisfies
and the point
on the line
satisfies
Let
and
be the circumcenters of the triangles
and
respectively. Prove that the lines
and
are concurrent.



















71 replies
Equation of integers
jgnr 3
N
2 hours ago
by KTYC
Source: Indonesia Mathematics Olympiad 2005 Day 1 Problem 2
For an arbitrary positive integer
, define
as the product of the digits of
(in decimal). Find all positive integers
such that
.





3 replies
Divisibility..
Sadigly 4
N
2 hours ago
by Solar Plexsus
Source: another version of azerbaijan nmo 2025
Just ignore this
4 replies
Surjective number theoretic functional equation
snap7822 3
N
2 hours ago
by internationalnick123456
Source: 2025 Taiwan TST Round 3 Independent Study 2-N
Let
be a function satisfying the following conditions:
[list=i]
[*] For all
, if
and
, then
;
[*]
is surjective.
[/list]
Find the maximum possible value of
.
Proposed by snap7822

[list=i]
[*] For all




[*]

[/list]
Find the maximum possible value of

Proposed by snap7822
3 replies
FE with devisibility
fadhool 0
2 hours ago
if when i solve an fe that is defined in the set of positive integer i found m|f(m) can i set f(m) =km such that k is not constant and of course it depends on m but after some work i find k=c st c is constant is this correct
0 replies
Many Equal Sides
mathisreal 3
N
2 hours ago
by QueenArwen
Source: Brazil EGMO TST 2023 #1
Let
be a triangle with
and
. Let
and
be the midpoints of
and
respectively. The point
is inside of
such that
is equilateral. Let
and
. Prove that
.













3 replies
LOTS of recurrence!
SatisfiedMagma 4
N
2 hours ago
by Reacheddreams
Source: Indian Statistical Institute Entrance UGB 2023/5
There is a rectangular plot of size
. This has to be covered by three types of tiles - red, blue and black. The red tiles are of size
, the blue tiles are of size
and the black tiles are of size
. Let
denote the number of ways this can be done. For example, clearly
because we can have either a red or a blue tile. Also
since we could have tiled the plot as: two red tiles, two blue tiles, a red tile on the left and a blue tile on the right, a blue tile on the left and a red tile on the right, or a single black tile.
[list=a]
[*]Prove that
for all
.
[*]Prove that
for all
.
[/list]
Here,
for integers
.







[list=a]
[*]Prove that


[*]Prove that


[/list]
Here,
![\[ \binom{m}{r} = \begin{cases}
\dfrac{m!}{r!(m-r)!}, &\text{ if $0 \le r \le m$,} \\
0, &\text{ otherwise}
\end{cases}\]](http://latex.artofproblemsolving.com/b/8/d/b8d653661e421db1fce7d93837e7bce31337bb30.png)

4 replies
combi/nt
blug 1
N
2 hours ago
by blug
Prove that every positive integer
can be written in the form
where
for some non-negative
such that
for every
.






1 reply
Inequality, inequality, inequality...
Assassino9931 9
N
2 hours ago
by ZeroHero
Source: Al-Khwarizmi Junior International Olympiad 2025 P6
Let
be real numbers such that
Find the smallest possible value of
.
Binh Luan and Nhan Xet, Vietnam

![\[ab^2+bc^2+ca^2=6\sqrt{3}+ac^2+cb^2+ba^2.\]](http://latex.artofproblemsolving.com/3/d/0/3d015292c249a69a44d5f923092201d7a271b896.png)

Binh Luan and Nhan Xet, Vietnam
9 replies
