%I A014117
%S A014117 1,2,6,42,1806
%N A014117 Numbers n such that m^(n+1) = m mod n holds for all m.
%C A014117 "Somebody incorrectly remembered Fermat's little theorem as saying that 
               the congruence a^{n+1} = a (mod n) holds for all a if n is prime" 
               (Zagier). The sequence gives the set of integers n for which this 
               property is in fact true.
%C A014117 If i = j (mod n), then m^i = m^j (mod n) for all m. The latter congruence 
               generally holds for any (m, n)=1 with i = j (mod k), k being the 
               order of m modulo n, i.e. the least power k for which m^k = 1 (mod 
               n). - Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 04 2002
%D A014117 J. Dyer-Bennet, "A Theorem in Partitions of the Set of Positive Integers", 
               Amer. Math. Monthly, 47(1940) pp. 152-4.
%H A014117 D. Zagier, <a href="http://www-groups.dcs.st-and.ac.uk/~john/Zagier/Problems.html">
               Problems posed at the St Andrews Colloquium, 1996</a>
%Y A014117 Sequence in context: A152479 A115961 A123137 this_sequence A054377 A007018 
               A100016
%Y A014117 Adjacent sequences: A014114 A014115 A014116 this_sequence A014118 A014119 
               A014120
%K A014117 nonn,fini,full,nice
%O A014117 1,2
%A A014117 David Broadhurst (D.Broadhurst(AT)open.ac.uk)