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Peter
12:05 PM
@Sahaj I found a solution for $n=6$ (!!) : $$[31699366920, 43719523705, 107614702584]$$
Sahaj
12:18 PM
Wow! That’s an amazing find.
good job!!
Peter
To clarify : I had the idea to enumerate over the gcd's which is much more efficient than enumerating over a,b,c. The gcd's uniquely determine a,b,c.
Sahaj
Right. So the conjecture is generally untrue I’m supposing. The cases $n=2$ and $n=3$ still seem to be of interest.
Peter
In fact, for those I did not find any solution (besides of course the case with equal entries , for which $n=a=b=c=2$ can be proven to be the only one)
I was surprised that this system even has a solution other than the "trivial" one.
Sahaj
12:34 PM
yes, me too
Peter
Do you have any idea how at least the case $n=2$ could be solved ?
5 hours later…
Martin Hopf
5:23 PM
Here is a
hot question
about abundant numbers.
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Martin Hopf's prime numbers
primes of the form (b^n^2-1)/(b^n-1)
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