Zsigmondy numbers: Difference between revisions

Line 234:

Zsigmondy(n, 7, 5): 2, 3, 109, 37, 6841, 13, 372709, 1513, 176149, 1661, 964249309, 1801, 47834153641, 75139, 3162961, 3077713, 115933787267041, 30133, 5689910849522509, 3949201

</pre>

=={{header|Mathematica}}/{{header|Wolfram Language}}==

Return the Zsigmondy-number to a,b,n integer:

zsigmondy[a_Integer, b_Integer, n_Integer] := (

If[

n == 1, Return[{a - b}], Return[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]]])

</syntaxhighlight>

Task:

zsigmondy[a_Integer, b_Integer, n_Integer] := (

If[

n == 1, Return[{a - b}], Return[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]]])

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}};

data1 = List["Zsigmondy:2,1,n", "Zsigmondy:3,1,n", "Zsigmondy:4,1,n",

"Zsigmondy:5,1,n", "Zsigmondy:6,1,n", "Zsigmondy:7,1,n",

"Zsigmondy:3,2,n", "Zsigmondy:5,3,n", "Zsigmondy:7,3,n",

"Zsigmondy:7,5,n"];

data2 = matrix;

Grid[Transpose@{data1, data2}~

Prepend~{"pair of numbers", "Zsigmondy numbers"},

Dividers -> {All, {1 -> True, 2 -> True}}]

</syntaxhighlight>

output:

Grid[{{"pair of numbers",

"Zsigmondy numbers"}, {"Zsigmondy:2,1,n", {{{1}, {3}, {7}, {5}, \

{31}, {1}, {127}, {17}, {73}, {11}}}},

{"Zsigmondy:3,1,n", {{{2}, {1}, {13}, {5}, {121}, {7}, {1093}, \

{41}, {757}, {61}}}},

{"Zsigmondy:4,1,n", {{{3}, {5}, {7}, {17}, {341}, {13}, {5461}, \

{257}, {1387}, {41}}}},

{"Zsigmondy:5,1,n", {{{4}, {3}, {31}, {13}, {781}, {7}, {19531}, \

{313}, {15751}, {521}}}},

{"Zsigmondy:6,1,n", {{{5}, {7}, {43}, {37}, {311}, {31}, \

{55987}, {1297}, {46873}, {1111}}}},

{"Zsigmondy:7,1,n", {{{6}, {1}, {19}, {25}, {2801}, {43}, \

{137257}, {1201}, {39331}, {2101}}}},

{"Zsigmondy:3,2,n", {{{1}, {5}, {19}, {13}, {211}, {7}, {2059}, \

{97}, {1009}, {11}}}},

{"Zsigmondy:5,3,n", {{{2}, {1}, {49}, {17}, {1441}, {19}, \

{37969}, {353}, {19729}, {421}}}},

{"Zsigmondy:7,3,n", {{{4}, {5}, {79}, {29}, {4141}, {37}, \

{205339}, {1241}, {127639}, {341}}}},

{"Zsigmondy:7,5,n", {{{2}, {3}, {109}, {37}, {6841}, {13}, \

{372709}, {1513}, {176149}, {1661}}}}},

Dividers -> {All, {1 -> True, 2 -> True}},

ItemSize -> {Automatic, Automatic}]

</syntaxhighlight>

=={{header|Perl}}==