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A070326
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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).
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0
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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