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A068209 Considering the congruence (x+1)^p - x^p == 1 (mod p^2) sequence gives values of p of the form 3k - 1 such there exist nontrivial solutions (x other than 0 or -1 modulo p). 3
59, 83, 179, 227, 419, 443, 701, 857, 887, 911, 929, 971, 977, 1091, 1109, 1193, 1217, 1223, 1259, 1283, 1289, 1439, 1487, 1493, 1613, 1637, 1811, 1847, 1901, 1997, 2003, 2087, 2243, 2423, 2477, 2579, 2591, 2729, 2777, 2969, 3089, 3137, 3191, 3203, 3251 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From Jianing Song, Apr 20 2019: (Start)

Note that nontrivial solutions always exist for primes of the form 3k + 1.

Equivalently, primes of the form 3k - 1 such that x^(p-1) == (x+1)^(p-1) == 1 (mod p^2) has solutions. (End)

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..74

K. S. Brown, On the Density of Some Exceptional Primes

CROSSREFS

Cf. A001220.

Sequence in context: A026050 A304356 A283146 * A139958 A097459 A145291

Adjacent sequences:  A068206 A068207 A068208 * A068210 A068211 A068212

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Mar 23 2002

EXTENSIONS

Definition corrected by Mike Oakes, Feb 12 2009

STATUS

approved

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Last modified April 8 04:26 EDT 2020. Contains 333312 sequences. (Running on oeis4.)