[seqfan] A280098 (A018253)
Don Reble
djr at nk.ca
Wed Mar 25 08:42:35 CET 2020
Seqfans:
> %C A280098 Conjecture: only the integers k in {1, 3, 4, 6, 8, 12, 24}
> have the property that [the sum of the divisors of (k*n-1)]/k is
> always an integer. - Robert G. Wilson v, Dec 25 2016
He's right.
My proof relates to self-inverse multiplicative groups;
those moduli are {2,3,4,6,8,12,24} (almost Wilson's set).
A018253 refers to many proofs, that those are the self-inverse groups.
One can easily prove that, using the fact that the map "x -> x mod m"
from any modulo-km group to the modulo-m group is onto.
But then I struggled to prove that fact. I finally got it:
enumerate the kernel of the mapping, compute the number of cosets.
But it seems like swatting a mosquito with an anvil.
Did I overlook something simple?
--
Don Reble djr at nk.ca
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