A354269 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.
1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 31098449, 34970654, 35236643, 43046721, 58883189, 73220005, 93295347, 102199060, 104911962, 105709929, 112028791, 112870007, 115196746, 117560414, 129140163, 144185176
Offset: 1
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Programs
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PARI
is(n) = my(p=11, q=1006003); Mod(n, p^2)^(p-1)==1 && Mod(n, q^2)^(q-1)==1
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Python
def ok(b): return pow(b, 10, 121)==1 and pow(b, 1006002, 1006003**2)==1 print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, May 25 2022
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