[/quote]
,
such that for all positive integers 
,![\[
f(mn) = \mathrm{lcm}(m, n) \cdot \gcd(f(m), f(n)),
\]](http://latex.artofproblemsolving.com/6/0/7/6071692e2716901e88cc1cfc19ed60388c10701d.png)
where 
and 
denote the least common multiple and the greatest common divisor of 
and 
,
has a closed walk of length at most 
passing through each edge of 
at least once.
satisfying the following condition: for any real numbers 
and 
,
is equal to 
or 
contains no term of the form 
and 
.
?
,
,
be a triangle with 
.
,
,
,
,
respectively. A circle 
passing through 
and tangent to 
and 
at 
and 
,
and 
are symmetric to 
meets 
and 
at 
and 
,
meets 
.
.
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this is my 100th post! i cant believe it. 
P.S. can everyone who reads this give it an upvote? thx!
P.S. can everyone who reads this give it an upvote? thx!
This post has been edited 1 time. Last edited by JohannIsBach, Mar 10, 2025, 4:08 PM
more posts to get to 1000!
more 2 go
