a/b + b/c + c/a = n (Extend A072716?)

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Forwarded message from Dave Rusin:

rusin at math.niu.edu schrieb am 16.07.2003, 23:16:48:
<<
> How far can A072716 now be extended without too much risk of missing 
> an early term? 
I believe you can extend the list comfortably into the low hundreds, 
with certain caveats: if the list given is in fact incorrect, then 
much more important parts of mathematics will be called into question 
than a simple sequence; specifically, if the list is presented as 
"complete, assuming the Birch-Swinnerton-Dyer conjecture", then should 
a counterexample be found, all algebraic geometers will stop dead in 
their tracks. 

How about if I prepare a careful summary of the algebraic-geometry 
approach to this problem, specifically flagging the "conditional"
entries 
on the list? Is anyone else in your mailing-list group working on 
that approach already? (No need for me to duplicate efforts.) 

dave
>>