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A070326
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).
0
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, 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, 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
OFFSET
1,1
COMMENTS
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).
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.
EXAMPLE
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.
MATHEMATICA
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}]]
CROSSREFS
Sequence in context: A388541 A011222 A157298 * A103711 A199435 A257898
KEYWORD
easy,nonn,tabl
AUTHOR
Gottfried Helms, May 11 2002
EXTENSIONS
Edited by Dean Hickerson, Jun 06 2002
STATUS
approved