A066340 Fermat's triangle: T(n,m) = m^phi(n) mod n; n >= 2; 1 <= m <= n-1, where phi is Euler's totient function.

1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 4, 3, 4, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 6, 1, 6, 5, 6, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 8, 1, 8, 7, 8, 1, 8, 1, 8, 1, 1, 1, 6, 1, 10, 6, 1, 1, 6, 10, 1, 6, 1, 1

Offset: 2

Author

Wouter Meeussen, Jan 01 2002

Keywords

• easy
• nonn
• tabl

Comments

Fermat's little theorem states that T(n,m)=1 for all m relatively prime to n.

Examples

			Triangle begins:
1;
1, 1;
1, 0, 1;
1, 1, 1, 1;
1, 4, 3, 4,  1;
1, 1, 1, 1,  1, 1;
1, 0, 1, 0,  1, 0, 1;
1, 1, 0, 1,  1, 0, 1, 1;
1, 6, 1, 6,  5, 6, 1, 6, 1;
1, 1, 1, 1,  1, 1, 1, 1, 1,  1;
1, 4, 9, 4,  1, 0, 1, 4, 9,  4, 1;
1, 1, 1, 1,  1, 1, 1, 1, 1,  1, 1, 1;
1, 8, 1, 8,  1, 8, 7, 8, 1,  8, 1, 8, 1;
1, 1, 6, 1, 10, 6, 1, 1, 6, 10, 1, 6, 1, 1;
		

Links

• Alois P. Heinz, Rows n = 2..201, flattened

Crossrefs

Cf. A000010.

Programs

Mathematica

Table[PowerMod[ #, EulerPhi[n], n]&/@ Range[n-1], {n, 2, 32} ]

PARI

T(n,k) = lift(Mod(k, n)^eulerphi(n));
tabl(nn) = for (n=2, nn, for (k=1, n-1, print1(T(n,k), ", ")); print); \\ Michel Marcus, Aug 13 2019