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Prime divisors of 68^112 - 1, listed with multiplicities.

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`%I #9 May 21 2016 22:52:43
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`%S 3,5,5,5,23,29,37,41,67,113,113,113,197,617,881,10193,103867,521497,
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`%T 938071,1106356357,1546157677,100343116693,518914006417,
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`%U 1145565031404704513,135178919999357237393881,620712448371732926474772025689944913040651041015217889164158638163856301549281
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`%N Prime divisors of 68^112 - 1, listed with multiplicities.
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`%C (68^112-1)/113 is the only known Fermat quotient q_p(b) = (b^(p-1)-1)/p with 1 < b < p and q_p(b) divisible by p^2.
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`%H G. P. Michon, <a href="http://www.numericana.com/data/68.htm">Prime Factorization of 68^112-1</a>.
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`%e 68^112 == 1 (mod 113^3), but 68^112 =/= 1 (mod 113^4), so 113 appears three times in the sequence.
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`%o (PARI) forprime(p=1, 68^112-1, my(k=1); while(Mod(68, p^k)^112==1, print1(p, ", "); k++))
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`%Y Cf. A172290, A242715.
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`%K nonn,fini,full
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`%O 1,1
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`%A _Felix FrÃ¶hlich_, May 14 2016
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