OFFSET
1,2
COMMENTS
A general formula for the isomorphism class of the group of units in any quotient ring of the polynomial ring F_p[x] (p prime) is given by Keith Kearnes in the Mathematics Stack Exchange link below.
LINKS
Mathematics Stack Exchange, Multiplicative group modulo polynomials.
EXAMPLE
Triangle begins
1;
2;
4;
2, 4;
2, 8;
2, 2, 8;
2, 4, 8;
2, 2, 4, 8;
2, 2, 4, 16;
2, 2, 2, 4, 16;
2, 2, 4, 4, 16;
2, 2, 2, 4, 4, 16;
2, 2, 2, 4, 8, 16;
2, 2, 2, 2, 4, 8, 16;
2, 2, 2, 4, 4, 8, 16;
2, 2, 2, 2, 4, 4, 8, 16;
2, 2, 2, 2, 4, 4, 8, 32;
...
MATHEMATICA
groupofunits2xn[e_] := Flatten[Table[{Table[2^(i + 1), {(Ceiling[e/2^i] - 2 Ceiling[e/2^(i + 1)] + Ceiling[e/2^(i + 2)])}]}, {i, 0, 10}]]; Prepend[Drop[Table[groupofunits2xn[n], {n, 1, 16}], 1], {1}]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Geoffrey Critzer, Aug 11 2024
STATUS
approved