Further
references collected from the mentioned articles:
(Richard
Fischer:)
[1] Wilfrid
Keller and Jörg Richstein
Fermat quotients qp(a) that are divisible by p
http://www1.uni-hamburg.de/RRZ/W.Keller/FermatQuotient.html
[2] Michael
Mossinghoff
Wieferich Prime Pairs, Barker Sequences, and Circulant Hadamard Matrices
http://www.cecm.sfu.ca/~mjm/WieferichBarker/
[3] R.
Ernvall and T. Metsänkylä
On the p-divisibility of fermat-quotients
Mathematics of Computation, Vol. 66, Number 219, July 1997, Pages 1353{1365 S
0025-5718(97)00843-0
http://www.ams.org/mcom/1997-66-219/S0025-5718-97-00843-0/S0025-5718-97-00843-0.pdf
[4] http://en.wikipedia.org/wiki/Wieferich_prime
[5] http://www.math.niu.edu/~rusin/known-math/98/1093
[6] http://www.asahi-net.or.jp/~KC2H-MSM/mathland/math11/fer_quo.htm
[7] http://home.earthlink.net/~oddperfect/FermatQuotients.html
(Andrew Granville)
1. J.W.L.
Glaisher,
On the residues of the sums of products of the first p–1 numbers and their
powers to modulus p2 or p3,
Quart. J. Math. Oxford 31 (1900), 321{353.
2. Paulo
Ribenboim,
Thirteen lectures on Fermat's Last Theorem,
Springer-Verlag, New York, 1979.
(Karl Dilcher)
[1] J.
W. L. Glaisher,
On the residues of the sums of products of the first p − 1 numbers and their
powers to modulus p2 or p3,
Quart. J. Math. Oxford 31 (1900), 321–353.
[2] A.
Granville,
The square of the Fermat quotient,
Integers: Electronic J. of Combinatorial Number Theory 4 (2004), #A22
(electronic).
[3] P.
Ribenboim,
13 Lectures on Fermat’s Last Theorem.
Springer-Verlag, New York, 1979.
(J. B. Dobson)
1. W. Johnson,
“On the nonvanishing of Fermat quotients (mod p),”
Journal für die Reine und Angewandte Mathematik 292 (1977): 196-200.
Available online at http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN243919689_0292
.
2. Wells
Johnson,
“On the p-Divisibility of the Fermat Quotients,”
Mathematics of Computation 32 (1978): 297-301.
3. J.
Knauer and J. Richstein,
“The continuing search for Wieferich primes,”
Mathematics of Computation 74 (2005): 1559-1563.
4. A. Rotkiewicz,
“Sur les nombres de Mersenne dépourvus de diviseurs carrés et sur les nombres
naturels n tels que n2 | 2n − 2,”
Matematički Većnik / Matematicki Vesnik 2(17) (1965): 78–80.
We first learned of this little-known paper through
various writings of Paulo Ribenboim.
5. Le
Roy J. Warren and Henry G. Bray,
“On the Square Freeness of Fermat and Mersenne Numbers,”
Pacific Journal of Mathematics 22 (1967): 563–4.
Available online at http://projecteuclid.org/handle/euclid.pjm/1102992105
.
6. F.G.
Dorais and D.W. Klyve,
Near Wieferich Primes up to 6.7 × 1015
[PDF]. Dated November 27, 2008.
Available online at http://www-personal.umich.edu/~dorais/docs/wieferich.pdf
.
(References given in Dorais/Klyve:)
1. N.
Beeger,
On a new case of the congruence 2p–1 – 1 (mod p2),
Messenger of Mathematics 51 (1922), 149{150.
2. N.
G. W. H. Beeger,
On the congruence 2p–1 – 1 (mod p2) and Fermat's last
theorem,
Nieuw Arch. Wiskde 20 (1939), 51{54. MR MR0000390 (1,65d)
3. J.
Brillhart, J. Tonascia, and P. Weinberger,
On the Fermat quotient,
Computers in number theory (Proc. Sci. Res. Council Atlas Sympos. No. 2,
Oxford, 1969),
Academic Press, London, 1971, pp. 213{222. MR MR0314736 (47 #3288)
4. R.
Brown and R. McIntosh,
http://www.loria.fr/~zimmerma/records/Wieferich.status
, 2001 (note: typo in link corrected
"loaria"->"loria", –G.H).
5. Richard
Crandall, Karl Dilcher, and Carl Pomerance,
A search for Wieferich and Wilson primes,
Math. Comp. 66 (1997), no. 217, 433{449. MR MR1372002 (97c:11004)
6. J.
Crump,
reported at http://www.spacefire.com/numbertheory/Wieferich.htm (link invalid)
website was not functioning at time of publication of this article., 2001.
(note: There is a web-archive version
saved at oct 2004 –G.H.
http://web.archive.org/web/20041010063342/http://www.spacefire.com/numbertheory/Wieferich.htm
)
7. C.
E. Fröberg,
Some computations with wilson and fermat remainders,
Math. Tables Aids Comput 12 (1958), 281.
8. C.
E. Fröberg,
On some number-theoretical problems treated with computers,
Computers in Mathematical Research,
North-Holland, Amsterdam, 1968, pp. 84{88. MR MR0241350 (39 #2690)
9. Joshua
Knauer and Jörg Richstein,
The continuing search for Wieferich primes,
Math. Comp 74 (2005), no. 251, 1559{1563 (electronic). MR MR2137018
(2006a:11006)
10. Sidney
Kravitz,
The congruence 2p–1 – 1(mod p2) for p < 100; 000,
Math. Comp. 14 (1960), 378. MR MR0121334 (22 #12073)
11. D.
H. Lehmer,
On Fermat's quotient, base two,
Math. Comp. 36 (1981), no. 153, 289{290. MR MR595064 (82e:10004)
12. Emma
Lehmer,
On congruences involving Bernoulli numbers and the quotients of Fermat and
Wilson,
Ann. of Math. (2) 39 (1938), no. 2, 350{360. MR MR1503412
13. W. Meissner,
Über die teilbarkeit von 2p-1 – 2 durch das quadrat der primzahl p =
1093,
Sitzungsberichte (1913), 663{667.
14. Peter
L. Montgomery,
Modular multiplication without trial division,
Math. Comp. 44 (1985), no. 170, 519{521. MR MR777282 (86e:11121)
15. Erna
H. Pearson,
On the congruences (p–1)! == –1 and 2p–1 – 1 (mod p2),
Math. Comp. 17 (1964), 194{195. MR MR0159780 (28 #2996)
16. Paul
Pritchard,
A sublinear additive sieve for finding prime numbers,
Comm. ACM 24 (1981), no. 1, 18{23. MR MR600730 (82c:10011)
17. Hans
Riesel,
Note on the congruence ap–1 = 1 (mod p2),
Math. Comp. 18 (1964), 149{150. MR MR0157928 (28 #1156)
18. Jonathan
P. Sorenson,
The pseudosquares prime sieve,
Algorithmic number theory, Lecture Notes in Comput. Sci., vol. 4076,
Springer, Berlin, 2006, pp. 193{207. MR MR2282925
(2007m:11168)
19. Zhi
Hong Sun and Zhi Wei Sun,
Fibonacci numbers and Fermat's last theorem,
Acta Arith. 60 (1992), no. 4, 371{388. MR MR1159353 (93e:11025)
20. A. Wieferich,
Zum letzten Fermat'schen Theorem,
J. Reine Angew. Math. 136 (1909), 293{ 302