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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.

%I A066340 #20 Aug 13 2019 05:01:14
%S A066340 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 A066340 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 A066340 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 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.
%C A066340 Fermat's little theorem states that T(n,m)=1 for all m relatively prime to n.
%H A066340 Alois P. Heinz, <a href="/A066340/b066340.txt">Rows n = 2..201, flattened</a>
%e A066340 Triangle begins:
%e A066340 1;
%e A066340 1, 1;
%e A066340 1, 0, 1;
%e A066340 1, 1, 1, 1;
%e A066340 1, 4, 3, 4,  1;
%e A066340 1, 1, 1, 1,  1, 1;
%e A066340 1, 0, 1, 0,  1, 0, 1;
%e A066340 1, 1, 0, 1,  1, 0, 1, 1;
%e A066340 1, 6, 1, 6,  5, 6, 1, 6, 1;
%e A066340 1, 1, 1, 1,  1, 1, 1, 1, 1,  1;
%e A066340 1, 4, 9, 4,  1, 0, 1, 4, 9,  4, 1;
%e A066340 1, 1, 1, 1,  1, 1, 1, 1, 1,  1, 1, 1;
%e A066340 1, 8, 1, 8,  1, 8, 7, 8, 1,  8, 1, 8, 1;
%e A066340 1, 1, 6, 1, 10, 6, 1, 1, 6, 10, 1, 6, 1, 1;
%t A066340 Table[PowerMod[ #, EulerPhi[n], n]&/@ Range[n-1], {n, 2, 32} ]
%o A066340 (PARI) T(n,k) = lift(Mod(k, n)^eulerphi(n));
%o A066340 tabl(nn) = for (n=2, nn, for (k=1, n-1, print1(T(n,k), ", ")); print); \\ _Michel Marcus_, Aug 13 2019
%Y A066340 Cf. A000010.
%K A066340 easy,nonn,tabl
%O A066340 2,12
%A A066340 _Wouter Meeussen_, Jan 01 2002