Higher-order residue ?

[Giovanni Resta]

I beg your pardon for asking a stupid question, but  (maybe it
is the hot sun of July) there is something very basilar
I do not get in the definition of these sequences:

A001133
Primes p such that 2 is a cubic residue modulo p, but not a higher-order residue.
43,109,157,...

and similarly sequences A001136, A115591, A001134, A001135.

I thought that
"a number t is a k-order residue modulo p if
there exist a number m such that m^k is congruent to t modulo p,
i.e. m^k=t (mod p).

So 2 is indeed a cubic residue mod 43, since 20^3=2 (mod 43).
But it seems to me it is also a 5-th residue, since 8^5=2 (mod 43)
and also a 9-th residue, since 26^9=2 (mod 43) and so on
for orders  11,13,15,17,19,23,25,27,29,31,33,37,39,41.
So, where I'm wrong in the interpretation of the definition
of the sequences above ?
Thanks,
giovanni.