A070597 Duplicate of A070474.

0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3

Offset: 0

Author

N. J. A. Sloane, May 13 2002

Keywords

• dead

Comments

a(n)=A070474(n) [Proof: n^5-n^3 == 0 (mod 12) is shown explicitly for n=0 to 11, then the induction n->n+12 for the 5th-order polynomial followed by binomial expansion of (n+12)^k concludes that the zero (mod 12) is periodically extended to the other integers.] - R. J. Mathar, Jul 23 2009

Crossrefs

Cf. A008960, A070474.

Programs

Mathematica

Table[Mod[n^5,12],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *)

Sage

[power_mod(n,7,12) for n in range(0, 100)] # Zerinvary Lajos, Oct 28 2009