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

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, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 2

Author

Alonso del Arte, Nov 13 2011

Keywords

• nonn
• easy
• tabl

Comments

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.

Examples

			The first seven rows are
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
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.
		

Crossrefs

Cf. A089072, A066340 (Fermat's triangle).

Programs

Mathematica

Column[Table[Mod[k^(n - 1), n], {n, 2, 13}, {k, n - 1}], Center] (* Nov 14 2011 *)