Zsigmondy numbers: Difference between revisions

Attributes[zsigmondy] = Listable;

zsigmondy[a_Integer, b_Integer, 1] := a - b /; a >= b;

zsigmondy[a_Integer, b_Integer, n_Integer] := (

hatvanyok = a^Range[n] - b^Range[n];

kishatvany = a^Range[n - 1] - b^Range[n - 1];

biggestelement = Part[hatvanyok, n];

divisors = Divisors[biggestelement];

divisorpairs = Join @@ (Thread[{#, kishatvany}] & /@ divisors);

coprimepairs = Select[divisorpairs, CoprimeQ[#[[1]], #[[2]]] &];

firstelement = coprimepairs[[All, 1]];

revesedelements = ReverseSort[firstelement];

Commonest[revesedelements, 1]) /; a >= b

l1 = Table[zsigmondy[2, 1, k], {k, Range[10]}];

l2 = Table[zsigmondy[3, 1, k], {k, Range[10]}];

l3 = Table[zsigmondy[4, 1, k], {k, Range[10]}];

l4 = Table[zsigmondy[5, 1, k], {k, Range[10]}];

l5 = Table[zsigmondy[6, 1, k], {k, Range[10]}];

l6 = Table[zsigmondy[7, 1, k], {k, Range[10]}];

l7 = Table[zsigmondy[3, 2, k], {k, Range[10]}];

l8 = Table[zsigmondy[5, 3, k], {k, Range[10]}];

l9 = Table[zsigmondy[7, 3, k], {k, Range[10]}];

l10 = Table[zsigmondy[7, 5, k], {k, Range[10]}];

matrix = {{l1}, {l2}, {l3}, {l4}, {l5}, {l6}, {l7}, {l8}, {l9}, {l10}};

data2 = matrix;