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
Examples
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
Programs
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Maple
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 -
Mathematica
Table[Select[Range[n], CoprimeQ[#, n] && IntegerQ[PowerMod[#, 1/3, n]] &], {n, 1, 20}] // Grid (* Geoffrey Critzer, Jan 04 2015 *) -
PARI
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]",")) ) ); ) }
Extensions
Edited by Don Reble, May 07 2006
Comments