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Topic
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Integrable function: + and - on every subinterval.
SPQ 3
N
by solyaris
Provide a function integrable on [a, b] such that f takes on positive and negative values on every subinterval (c, d) of [a, b]. Prove your function satisfies both conditions.
3 replies
![\[\sum_{m=1}^\infty\sum_{n=1}^\infty\dfrac{m^2n}{3^m(n3^m+m3^n)}.\]](http://latex.artofproblemsolving.com/7/d/6/7d6247fbcfd6eac156ce774f727d7e95c470de52.png)
Find the greatest possible value of the expression
BEHZOD_UZ 1
N
by alexheinis
Source: Yandex Uzbekistan Coding and Math Contest 2025
Let 
be complex numbers with 
. Find the greatest possible value of the expression 
be complex numbers with 
. Find the greatest possible value of the expression 
1 reply
![$\underset{n\to \infty }{\mathop{\lim }}\,\sqrt[n]{lcm(1,2,3,...,n)}=e$](http://latex.artofproblemsolving.com/a/1/3/a139e5cb990f3386de109c701f8edc71b4054712.png)
combinatorics
Hello_Kitty 2
N
by Hello_Kitty
How many 
digit numbers are there
- not including the sequence
?
- not including the sequences and 
?
digit numbers are there- not including the sequence
?- not including the sequences
and 
?
2 replies
Sequence of functions
Squeeze 2
N
by Hello_Kitty
Q) let 
and 
then is this uniformly convergence on 
comment on uniformly convergence on ![$[0,1]$](//latex.artofproblemsolving.com/e/8/6/e861e10e1c19918756b9c8b7717684593c63aeb8.png)
where in general it is should be uniformly convergence.
My I am trying with some contradicton method like chose
and trying to solve
Next take a in (0,1) and chose a= 2^1/N but not solution
How to solve like this way help.
and 
then is this uniformly convergence on 
comment on uniformly convergence on ![$[0,1]$](http://latex.artofproblemsolving.com/e/8/6/e861e10e1c19918756b9c8b7717684593c63aeb8.png)
where in general it is should be uniformly convergence.My I am trying with some contradicton method like chose
and trying to solve
Next take a in (0,1) and chose a= 2^1/N but not solution
How to solve like this way help.
2 replies
A in M2(prime), A=B^2 and det(B)=p^2
jasperE3 1
N
by KAME06
Source: VJIMC 2012 1.2
Determine all 
integer matrices 
having the following properties:
the entries of are (positive) prime numbers,
there exists a integer matrix 
such that 
and the determinant of is the square of a prime number.
integer matrices 
having the following properties:
the entries of are (positive) prime numbers,
there exists a integer matrix 
such that 
and the determinant of is the square of a prime number.1 reply
Equation over a finite field
loup blanc 1
N
by alexheinis
Find the set of 
such that the equation in the unknown 
:
admits 
roots: 
s.t. 
.
such that the equation in the unknown 
:
admits 
roots: 
s.t. 
.
1 reply
Integration Bee Kaizo
Calcul8er 51
N
by BaidenMan
Hey integration fans. I decided to collate some of my favourite and most evil integrals I've written into one big integration bee problem set. I've been entering integration bees since 2017 and I've been really getting hands on with the writing side of things over the last couple of years. I hope you'll enjoy!
51 replies
