A273085 Prime divisors of 68^112 - 1, listed with multiplicities.

3, 5, 5, 5, 23, 29, 37, 41, 67, 113, 113, 113, 197, 617, 881, 10193, 103867, 521497, 938071, 1106356357, 1546157677, 100343116693, 518914006417, 1145565031404704513, 135178919999357237393881, 620712448371732926474772025689944913040651041015217889164158638163856301549281

Offset: 1

Author

Felix Fröhlich, May 14 2016

Keywords

• nonn
• fini
• full

Comments

(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.

Examples

			68^112 == 1 (mod 113^3), but 68^112 =/= 1 (mod 113^4), so 113 appears three times in the sequence.
		

Links

• G. P. Michon, Prime Factorization of 68^112-1.

Crossrefs

Cf. A172290, A242715.

Programs

PARI

forprime(p=1, 68^112-1, my(k=1); while(Mod(68, p^k)^112==1, print1(p, ", "); k++))