OFFSET
0,2
COMMENTS
Because a(39) = 78, the Legendre symbol (3/79) = -1, meaning that 3 is not a quadratic residue of 79. Furthermore, it means that 3 is prime in Z[sqrt(79)]. - Alonso del Arte, Oct 01 2012
REFERENCES
I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).
FORMULA
EXAMPLE
a(4) = 2 because 3^4 = 81 and 81 - 79 = 2.
MAPLE
[ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];
MATHEMATICA
Table[Mod[3^n, 79], {n, 0, 60}] (* Alonso del Arte, Oct 01 2012 *)
PowerMod[3, Range[0, 100], 79] (* Harvey P. Dale, Feb 21 2024 *)
PROG
(PARI) a(n)=lift(Mod(3, 79)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(3, n, 79): n in [0..100]]; // G. C. Greubel, Oct 17 2018
(Python) for n in range(0, 100): print(int(pow(3, n, 79)), end=' ') # Stefano Spezia, Oct 17 2018
(GAP) List([0..60], n->PowerMod(3, n, 79)); # Muniru A Asiru, Oct 17 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved