[seqfan] Re: A181189

Don Reble djr at nk.ca
Fri Oct 6 03:22:15 CEST 2023

> ... the sequence is well defined ... if the checks [are] performed by
> drawing randomly numbers of this unknown multiset until all but one of
> the known multisets can be excluded.

    That's my take. Using just orders, not group elements, it doesn't
    matter whether 
> comparison [is] an allowed operation
    nor whether
> computing g_i, g_i^2, g_i^3 etc
    is possible.

> Imagine that ... order is obtained by computing g_i, g_i^2, g_i^3 etc
> until g_i^o=e (then o is the order, e the unit element).
> ...how would one know that one of the powers "hits" e if
> e has not been identified earlier?

    To identify the identity, go until the powers of G repeat.
    If g^x = g, then g^(x-1) = e.
    Alternatively, "x op x = x" ifAndOnlyIf X is the identity.

Don Reble  djr at nk.ca

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