A200323 - OEIS

A200323

For each composite m = A002808(n), a(n) is the smallest number k for which the equation x^m + (x+k)^m = (x+k+1)^m (mod m) has no solution, where x = 0..m-1.

%I #5 Mar 30 2012 18:36:00

%S 2,3,2,3,3,2,2,1,2,3,2,7,2,2,1,2,3,2,3,2,1,2,1,2,3,1,2,3,2,3,4,2,2,3,

%T 2,2,3,1,2,1,3,2,2,3,2,4,3,2,1,3,2,2,1,2,2,2,2,3,2,2,3,3,2,2,3,3,2,3,

%U 4,1,2,2,1,2,3,2,7,3,2,3,2,2,3,1,2,1,2

%N For each composite m = A002808(n), a(n) is the smallest number k for which the equation x^m + (x+k)^m = (x+k+1)^m (mod m) has no solution, where x = 0..m-1.

%e a(12) = 7 because A002808(12) = 21 and the equation x^21 + (x+7)^21 = (x+8)^21 (mod 21)has no solution.

%p for n from 1 to 120 do: i:=0:for k from 1 to 500 while(i=0) do :ii:=0:for x from 0 to n-1 do:if x^n+(x+k)^n -(x+k+1)^n mod n =0 then ii:=ii+1:else fi:od: if ii=0 then i:=1:printf(`%d, `,k):else fi:od:od:

%Y Cf. A002808, A200046.

%K nonn

%O 1,1

%A _Michel Lagneau_, Nov 16 2011