%I
%S 1,1,1,1,0,3,1,1,1,1,1,2,3,4,5,1,1,1,1,1,1,1,0,3,0,5,0,7,1,4,0,7,7,0,
%T 4,1,1,2,3,4,5,6,7,8,9,1,1,1,1,1,1,1,1,1,1,1,8,3,4,5,0,7,8,9,4,11,1,1,
%U 1,1,1,1,1,1,1,1,1,1
%N Triangle read by rows: T(n, k) = mod(k^(n  1), n), where 1 <= k < n.
%C Per Fermat's Little theorem, if n is prime, then row n is all 1s. However, if n is composite, that does not necessarily guarantee that the first column 1 is the only one in the row.
%e The first seven rows are
%e 1
%e 1, 1
%e 1, 0, 3
%e 1, 1, 1, 1
%e 1, 2, 3, 4, 5
%e 1, 1, 1, 1, 1, 1
%e 1, 0, 3, 0, 5, 0, 7
%e We observe that the tenth row consists of the numbers 1 to 9 in order. In base 10, the least significant digit of n^9 is the same as that of n.
%t Column[Table[Mod[k^(n  1), n], {n, 2, 13}, {k, n  1}], Center] (* Nov 14 2011 *)
%Y Cf. A089072, A066340 (Fermat's triangle).
%K nonn,easy,tabl
%O 2,6
%A _Alonso del Arte_, Nov 13 2011
