A096087 -id:A096087 - cp's OEIS frontend

A096107 Triangle read by rows: row n lists cubic residues modulo n.

1, 1, 2, 1, 3, 1, 2, 3, 4, 1, 5, 1, 6, 1, 3, 5, 7, 1, 8, 1, 3, 7, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 5, 7, 11, 1, 5, 8, 12, 1, 13, 1, 2, 4, 7, 8, 11, 13, 14, 1, 3, 5, 7, 9, 11, 13, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 17, 1, 7, 8, 11, 12, 18, 1, 3, 7, 9, 11, 13, 17, 19, 1, 8

Offset: 2

Cino Hilliard, Jul 22 2004

Row n has A087692(n) terms. - Robert Israel, Jan 04 2015

			1;
1,2;
1,3;
1,2,3,4;
1,5;
1,6;
1,3,5,7;
1,8;
1,3,7,9;
Row 5 contains 1,2,3,4 because (in mod 5)  1^3 = 1, 3^3 = 2, 2^3 = 3, and 4^3 = 4. - _Geoffrey Critzer_, Jan 07 2015

Cf. A087692, A096087.

for n from 2 to 30 do
  op({seq(`if`(igcd(i,n)=1,i^3 mod n,NULL),i=1..n-1)})
# if using Maple 11 or earlier, replace this by
#   op(sort(convert({seq(`if`(igcd(i,n)=1,i^3 mod n,NULL),i=1..n-1)},list)))
od; # Robert Israel, Jan 04 2015

Table[Select[Range[n],
   CoprimeQ[#, n] && IntegerQ[PowerMod[#, 1/3, n]] &], {n, 1, 20}] // Grid
(* Geoffrey Critzer, Jan 04 2015 *)

maybecubegcd1(n) = { for(x=2,n, b=floor(x-1); a=vector(b+1); for(y=1,b, z=y^3%x; if(z<>0, a[y]=z; ) ); s=vecsort(a); c=1; for(j=2,b+1, if(s[j]<>s[j-1], c++; if(gcd(s[j],x)==1,print1(s[j]",")) ) ); ) }

Edited by Don Reble, May 07 2006

A337596 Largest m such that k^n (mod m) is always either 0, +1, or -1.

Original entry on oeis.org

3, 5, 9, 16, 11, 13, 4, 32, 27, 25, 23, 16, 4, 29, 31, 64, 4, 37, 4, 41, 49, 23, 47, 32, 11, 53, 81, 29, 59, 61, 4, 128, 67, 8, 71, 73, 4, 8, 79, 41, 83, 49, 4, 89, 31, 47, 4, 97, 4, 125, 103, 53, 107, 109, 121, 113, 9, 59, 4, 61, 4, 8, 127, 256, 131, 67, 4, 137

Offset: 1

Elliott Line, Sep 02 2020

nonn

For a given n, for all k, k^n mod a(n) will always be either 0, 1 or a(n)-1. This will not be true for numbers larger than a(n).

It appears that a(m) = 4 for m in A045979. - Michel Marcus, Sep 04 2020

			For n = 5 all fifth powers of natural numbers: 1,32,243,1024, etc. are either a multiple of 11, or 1 greater or 1 less than a multiple of 11. There is no greater number than 11 for which all fifth powers are at most 1 different from a multiple. So a(5) = 11.

Cf. A010872, A070430, A167176, A000035, A070596, A070636, A109718.

Cf. residues: A096008 (for n=2), A096087 (for n=3).

More terms from Michel Marcus, Sep 04 2020

cp's OEIS Frontend

A096107 Triangle read by rows: row n lists cubic residues modulo n.

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