A066340 - OEIS

%I #20 Aug 13 2019 05:01:14

%S 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,

%T 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,

%U 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

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

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

%H Alois P. Heinz, <a href="/A066340/b066340.txt">Rows n = 2..201, flattened</a>

%e Triangle begins:

%e 1;

%e 1, 1;

%e 1, 0, 1;

%e 1, 1, 1, 1;

%e 1, 4, 3, 4,  1;

%e 1, 1, 1, 1,  1, 1;

%e 1, 0, 1, 0,  1, 0, 1;

%e 1, 1, 0, 1,  1, 0, 1, 1;

%e 1, 6, 1, 6,  5, 6, 1, 6, 1;

%e 1, 1, 1, 1,  1, 1, 1, 1, 1,  1;

%e 1, 4, 9, 4,  1, 0, 1, 4, 9,  4, 1;

%e 1, 1, 1, 1,  1, 1, 1, 1, 1,  1, 1, 1;

%e 1, 8, 1, 8,  1, 8, 7, 8, 1,  8, 1, 8, 1;

%e 1, 1, 6, 1, 10, 6, 1, 1, 6, 10, 1, 6, 1, 1;

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

%o (PARI) T(n,k) = lift(Mod(k, n)^eulerphi(n));

%o tabl(nn) = for (n=2, nn, for (k=1, n-1, print1(T(n,k), ", ")); print); \\ _Michel Marcus_, Aug 13 2019

%Y Cf. A000010.

%K easy,nonn,tabl

%O 2,12

%A _Wouter Meeussen_, Jan 01 2002