Y by
Let 
and let 
be reals such that 
Prove
and let 
be reals such that 
Prove
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Tilted Students Thoroughly Splash Tiger part 2
DottedCaculator 18
N
by MathLuis
Source: ELMO 2024/5
In triangle 
with 
and 
, let 
be the midpoint of 
. Choose point 
on the extension of 
past 
and point 
on segment 
such that lies on 
. Let 
be on the opposite side of 
from 
such that 
and 
. Let 
intersect the circumcircle of 
again at 
, and let 
intersect the circumcircle of 
again at 
. Prove that , 
, and 
are collinear.
Tiger Zhang
with 
and 
, let 
be the midpoint of 
. Choose point 
on the extension of 
past 
and point 
on segment 
such that lies on 
. Let 
be on the opposite side of 
from 
such that 
and 
. Let 
intersect the circumcircle of 
again at 
, and let 
intersect the circumcircle of 
again at 
. Prove that , 
, and 
are collinear.Tiger Zhang
18 replies
Putnam 1958 February A5
sqrtX 4
N
by Safal
Source: Putnam 1958 February
Show that the integral equation
has at most one solution continuous for 
has at most one solution continuous for 
4 replies
Miklós Schweitzer 1956- Problem 1
Coulbert 1
N
by NODIRKHON_UZ
1. Solve without use of determinants the following system of linear equations:
(
),
where
is a fixed real number. (A. 7)
(
),where
is a fixed real number. (A. 7)
1 reply
D1021 : Does this series converge?
Dattier 3
N
by Dattier
Source: les dattes à Dattier
Is this series 
converge?
converge?
3 replies
If a matrix exponential is identity, does it follow the initial matrix is zero?
bakkune 5
N
by loup blanc
This might be a really dumb question, but I have neither a rigorous proof nor a counter example.
For any square matrix
, define
where 
is the identity matrix. If for some matrix that 
is identity, does it follow that is zero?
For any square matrix
, define
where 
is the identity matrix. If for some matrix that 
is identity, does it follow that is zero?
5 replies
Range of 2 parameters and Convergency of Improper Integral
Kunihiko_Chikaya 3
N
by Mathzeus1024
Source: 2012 Kyoto University Master Course in Mathematics
Let 
be real numbers. Find the ranges of such that the improper integral 
converges.
be real numbers. Find the ranges of such that the improper integral 
converges.
3 replies
Matrix Row and column relation.
Schro 6
N
by Schro
If ith row of a matrix A is dependent,Then ith column of A is also dependent and vice versa .
Am i correct...
Am i correct...
6 replies
A small problem in group theory
qingshushuxue 2
N
by qingshushuxue
Assume that 
are group. If 
, prove that 
or 
.
where
are group. If 
, prove that 
or 
. where
2 replies
Putnam 1958 February A4
sqrtX 2
N
by centslordm
Source: Putnam 1958 February
If 
are complex numbers such that
and if 
denotes the sum of all products of these 
numbers taken 
at a time, prove that
whenever the denominator of the left-hand side is different from 
.
are complex numbers such that
and if 
denotes the sum of all products of these 
numbers taken 
at a time, prove that
whenever the denominator of the left-hand side is different from 
.
2 replies
analysis
Hello_Kitty 2
N
by Hello_Kitty
what is the range of 
for any positive reals satifying 
?
for any positive reals satifying 
?
2 replies
Putnam 1958 February A1
sqrtX 2
N
by centslordm
Source: Putnam 1958 February
If 
are real number satisfying
show that the equation 
has at least one real root.
are real number satisfying
show that the equation 
has at least one real root.
2 replies
n variables with n-gon sides
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G
H
Source: Own
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