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%I #6 Jun 24 2014 01:08:24
%S 4,7,7,8,13,4,7,7,19,7,4,9,7,13,4,13,13,7,13,7,7,9,19,4,9,8,37,4,7,7,
%T 13,7,9,19,13,7,4,7,8,7,4,13,13,7,4,9,13,7,9,7,7,9,13,31,7,7,7,4,7,9,
%U 31,4,7,7,13,4,31,13,7,13,7,7,13,13,19,7,13,7,4,25,7,9,4,7,8,27,4,7,19
%N Upper triangular array giving for each (x,y) the minimum modulus m such that x^3+y^3 is not congruent to a cube (mod m).
%C The first few values of n and their corresponding values of x and y are (n,x,y) = (1,1,1), (2,2,1), (3,2,2), (4,3,1), (5,3,2), (6,3,3).
%C The modulus a(n) can be used to verify that x^3+y^3 is not a cube, so does not violate Fermat's Last Theorem for the exponent 3.
%e a(3)=7: n=3 corresponds to x=y=2; 2^3+2^3=16, which is not congruent to a cube (mod 7), but is congruent to a cube (mod m) for every m from 1 to 6.
%t cubes[m_] := cubes[m]=Union[Table[Mod[n^3, m], {n, 0, m-1}]]; a[x_, y_] := For[m=1, True, m++, If[ !MemberQ[cubes[m], Mod[x^3+y^3, m]], Return[m]]]; Flatten[Table[a[x, y], {x, 1, 15}, {y, 1, x}]]
%K easy,nonn,tabl
%O 1,1
%A _Gottfried Helms_, May 11 2002
%E Edited by _Dean Hickerson_, Jun 06 2002
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