A070667 -id:A070667 - cp's OEIS frontend

A070673 Smallest m in range 2..n-1 such that m^8 == 1 mod n, or 1 if no such number exists.

1, 1, 2, 3, 2, 5, 6, 3, 8, 3, 10, 5, 5, 13, 2, 3, 2, 17, 18, 3, 8, 21, 22, 5, 7, 5, 26, 13, 12, 7, 30, 3, 10, 9, 6, 17, 6, 37, 5, 3, 3, 13, 42, 21, 8, 45, 46, 5, 48, 7, 2, 5, 23, 53, 12, 13, 20, 17, 58, 7, 11, 61, 8, 7, 8, 23, 66, 9, 22, 13, 70, 17, 10, 31, 7, 37

Offset: 1

N. J. A. Sloane, May 08 2002

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A070667.

a:= proc(n) local m;
      for m from 2 to n-1 do
        if m &^ 8 mod n = 1 then return m fi
      od; 1
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 29 2014

a[n_] := Module[{m}, For[m = 2, m <= n-1, m++,
    If[PowerMod[m, 8, n] == 1, Return[m]]]; 1];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Mar 06 2024 *)

a(n) = {for (m=2, n-1, if (lift(Mod(m, n)^8) == 1, return (m));); return (1);} \\ Michel Marcus, Jun 29 2014

A070674 Smallest m in range 2..n-1 such that m^9 == 1 mod n, or 1 if no such number exists.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 3, 9, 1, 1, 1, 7, 4, 1, 4, 1, 1, 1, 1, 3, 4, 9, 1, 1, 5, 1, 1, 1, 11, 13, 7, 5, 16, 1, 1, 25, 6, 1, 16, 1, 1, 1, 18, 1, 1, 9, 1, 7, 1, 9, 4, 1, 1, 1, 13, 5, 4, 1, 16, 1, 29, 1, 1, 11, 1, 25, 2, 7, 1, 5, 23, 55, 23, 1, 10, 1, 1, 25, 1

Offset: 1

N. J. A. Sloane, May 08 2002

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A070667.

a:= proc(n) local m;
      for m from 2 to n-1 do
        if m &^ 9 mod n = 1 then return m fi
      od; 1
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 29 2014

a[n_] := Module[{m}, For[m = 2, m <= n-1, m++, If[PowerMod[m, 9, n] == 1, Return[m]]]; 1];
Array[a, 100] (* Jean-François Alcover, Nov 18 2020 *)

a(n) = {for (m=2, n-1, if (lift(Mod(m, n)^9) == 1, return (m));); return (1);} \\ Michel Marcus, Jun 29 2014

cp's OEIS Frontend

A070673 Smallest m in range 2..n-1 such that m^8 == 1 mod n, or 1 if no such number exists.

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