be a function which is continuous on ![\( [0,1] \)](http://latex.artofproblemsolving.com/0/1/0/01026be294289be8f090c7b2586dde64a0d5b479.png)
and differentiable on 
,
.
such that 
.
such that 
.
be a positive integer. Prove that 
is a permutation polynomial mod 
a permutation polynomial mod 
is bijective.
such that 
?
.
as the average of all 
for 
.![\[ a = \lim_{k \to \infty} \sup_{n \geq k} \frac{a_n}{n^4} .\]](http://latex.artofproblemsolving.com/5/2/d/52d93af7aafa6657689246d9a74c8eb05d96efa3.png)
with 
such that
and 
and 
with equal radii intersect at P and Q. Points B and C are located on the circle
The intersection point of the circumcircles of triangles XPC and YPB is called S. Prove that BC, XY and QS are concurrent.
? (there is an easy workaround)
what is range of values of 
what is range of values of 
be a sequence of nonnegative real numbers whose sum is 
.![$$\sum_{k=1}^\infty \left(k\cdot (3k+2) \cdot 2^{-k} \cdot \sqrt[k]{a_1a_2\dots a_k}\right).$$](http://latex.artofproblemsolving.com/2/d/f/2df5179ce532077733530d5e9f1266c22d1cdb7d.png)
Y by
Summary of the problem: I can upvote when in the forum but when looking at the thread through my feed I can't upvote posts (or do anything except quote)
Steps to reproduce:
1. go to like alcumus or something where you can see ur feed
2. click on a thread
3. no upvote button
...
Frequency: tried refreshing once, didnt work
Operating system(s): Windows
Browser(s), including version: Bing
Additional information: Will add screenshot in a sec
Steps to reproduce:
1. go to like alcumus or something where you can see ur feed
2. click on a thread
3. no upvote button
...
Frequency: tried refreshing once, didnt work
Operating system(s): Windows
Browser(s), including version: Bing
Additional information: Will add screenshot in a sec
Attachments:
This post has been edited 3 times. Last edited by stjwyl, Mar 31, 2025, 1:39 AM
