[/quote]
,
be a positive integer and 
be a polynomial with integer coefficients such that 
.
is divisible 
.
and 
be two infinite sequences of integers. Prove that there exists an infinite sequence of integers 
such that for any positive integer 
,![\[
\sum_{k|n} k \cdot z_k^{\frac{n}{k}} = \left( \sum_{k|n} k \cdot x_k^{\frac{n}{k}} \right) \cdot \left( \sum_{k|n} k \cdot y_k^{\frac{n}{k}} \right).
\]](http://latex.artofproblemsolving.com/2/5/9/259ee32c89befe7a3ee2797e0d5b1df1c3066cf6.png)
be an infinite sequence and 
,
for all 
.
is a perfect square for all 
.
such that for all real 
![\[f(x+f(y))=f(x+y)+y\]](http://latex.artofproblemsolving.com/1/e/2/1e2fef35ee53cd3224527f672b9edbb7a5293fad.png)
be non-negative real variables with 
Prove that
Equality holds iff 
or 
where 
.
.
and 
are divisible by 
.
be a triangle with 
.
and 
lie on sides 
and 
,
and 
.
and 
meet at 
.
,
,
,
to all have integer lengths.
Y by Pengu14, hsuya1
Hi Mods,
Could you please let me know why my replies about leaks were removed? Were there any inappropriate words in my response? I spent a valuable hour of my time writing those replies, and I find it frustrating that only the post supporting MAA was kept while all other perspectives were removed.
Is the goal to turn this forum into a sinking ship, just like MAA? Why can't people express their honest opinions on this critical issue and push for much-needed change?
I understand that my post may be removed again, but I would appreciate a reasonable explanation—either here or via PM.
Thank you!
Could you please let me know why my replies about leaks were removed? Were there any inappropriate words in my response? I spent a valuable hour of my time writing those replies, and I find it frustrating that only the post supporting MAA was kept while all other perspectives were removed.
Is the goal to turn this forum into a sinking ship, just like MAA? Why can't people express their honest opinions on this critical issue and push for much-needed change?
I understand that my post may be removed again, but I would appreciate a reasonable explanation—either here or via PM.
Thank you!
