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Numbers b such that b^(11-1) == 1 (mod 11^2) and b^(1006003-1) == 1 (mod 1006003^2), i.e., common Wieferich bases of 11 and 1006003.
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%I #23 May 30 2022 01:47:42

%S 1,3,9,27,81,243,729,2187,6561,19683,59049,177147,531441,1594323,

%T 4782969,14348907,31098449,34970654,35236643,43046721,58883189,

%U 73220005,93295347,102199060,104911962,105709929,112028791,112870007,115196746,117560414,129140163,144185176

%N Numbers b such that b^(11-1) == 1 (mod 11^2) and b^(1006003-1) == 1 (mod 1006003^2), i.e., common Wieferich bases of 11 and 1006003.

%C A000244 is a subsequence.

%o (PARI) is(n) = my(p=11, q=1006003); Mod(n, p^2)^(p-1)==1 && Mod(n, q^2)^(q-1)==1

%o (Python)

%o def ok(b): return pow(b, 10, 121)==1 and pow(b, 1006002, 1006003**2)==1

%o print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, May 25 2022

%Y Cf. A000244, A014127, A247208.

%K nonn

%O 1,2

%A _Felix Fröhlich_, May 25 2022