OFFSET
1,4
COMMENTS
For primes p > 3, there is always a solution to the equation.
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, Second Edition, Springer, 1994, Section F9.
W. P. Zhang, On a problem of Brizolis, Pure Appl. Math., 11(suppl.):1-3, 1995.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
J. Holden and P. Moree, New conjectures and results for small cycles of the discrete logarithm, arXiv:math/0305305 [math.NT], 2003, published in: High Primes and Misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams, AMS, 2004, pp. 245-254.
EXAMPLE
a(1) = 1 because p = 2, g = 1, and 1^1 == 1 (mod 2).
a(3) = 1 because p = 5 and 2^3 == 3 (mod 5) is the only solution.
MATHEMATICA
Table[p=Prime[n]; x=PrimitiveRoot[p]; prims=Select[Range[p-1], GCD[ #1, p-1]==1&]; s=0; Do[g=PowerMod[x, prims[[i]], p]; Do[If[PowerMod[g, h, p]==h, s++ ], {h, p-1}], {i, Length[prims]}]; s, {n, 3, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Jun 03 2003
EXTENSIONS
a(1) corrected by N. J. A. Sloane, Apr 14 2024 at the suggestion of José Hdz. Stgo.
STATUS
approved