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 A200146 Triangle read by rows: T(n, k) = mod(k^(n - 1), n), where 1 <= k < n. 1

%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

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Last modified December 16 00:33 EST 2019. Contains 330013 sequences. (Running on oeis4.)