

A090968


Primes p such that p^2 divides 19^(p1)  1.


10




OFFSET

1,1


COMMENTS

Primes p such that p divides the Fermat quotient of p (with base 19). The Fermat quotient of p with base a denotes the integer q_p(a) = ( a^(p1)  1) / p, where p is a prime which does not divide the integer a.  C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 20 2005
No further terms up to 3.127*10^13.


REFERENCES

J.M. De Koninck, Ces nombres qui nous fascinent, Entry 43, p. 17, Ellipses, Paris 2008.
Paulo Ribenboim, "The Little Book Of Big Primes," SpringerVerlag, NY 1991, page 170.
Roozbeh Hazrat, Mathematica:A ProblemCentered Approach, Springer 2010, pp. 39, 171


LINKS

Table of n, a(n) for n=1..6.
C. Caldwell, Fermat quotient
W. Keller and J. Richstein Fermat quotients q_p(a) that are divisible by p


MATHEMATICA

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ p = NextPrim[p]; If[PowerMod[19, p  1, p^2] == 1, Print[p]], {n, 1, 2*10^8}]
Select[Prime[Range[4*10^6]], PowerMod[19, #1, #^2]==1&] (* Harvey P. Dale, Nov 08 2017 *)


CROSSREFS

Cf. A001220, A014127, A123692, A123693, A128667, A128668, A128669, A039951, A096082
Sequence in context: A174241 A289556 A086208 * A020641 A062736 A257716
Adjacent sequences: A090965 A090966 A090967 * A090969 A090970 A090971


KEYWORD

nonn,hard,more


AUTHOR

Robert G. Wilson v, Feb 27 2004


EXTENSIONS

Third reference added by Harvey P. Dale, Oct. 17 2011


STATUS

approved



