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Old 2020-08-03, 08:35   #10
Batalov
 
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Mar 2008
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We had a forum member about a decade ago who drilled into residue pathways/topology/cycles but he has left many years ago and left all that quite unfinished. (Tony "T.Rex")
He had some conjectures but as far as I remember those ended up broken.
(Including one about a Wagstaff number test.)

One can search forum way back, using Search / Advanced / Search by User Name, and search for his threads, such as DiGraph for LLT, LLT Cycles, LLT Tree... there is probably something of interest (just don't assume those things right ... or wrong), pick and chose what is useful.
https://mersenneforum.org/showthread.php?t=5935
https://mersenneforum.org/showthread.php?t=10670
...and more
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