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A169618
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Table with T(n,k) = the number of ways to represent k as the sum of a square and a cube modulo n.
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1
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1, 2, 2, 3, 3, 3, 6, 6, 2, 2, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 11, 8, 12, 2, 6, 3, 12, 20, 4, 4, 12, 4, 4, 4, 15, 15, 6, 6, 6, 6, 6, 6, 15, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 18, 18, 6, 6, 18, 18, 6, 6, 18, 18, 6, 6, 13, 11, 18, 8, 20, 15, 6
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OFFSET
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1,2
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COMMENTS
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The top left corner is T(1,0).
It appears that this table does not contain any 0's.
It appears that row n is constant iff n is squarefree, and no prime divisor of n is == 1 (mod 6). It is not hard to show that such rows are constant, since the cubes are equi-distributed in such moduli.
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LINKS
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EXAMPLE
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The 6 ways to represent 0 (mod 4) are 0^2+0^3, 0^2+2^3, 1^2+3^3, 2^2+0^3, 2^2+2^3, and 3^2+3^3.
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PROG
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(PARI) al(n)=local(v); v=vector(n); for(i=0, n-1, for(j=0, n-1, v[(i^2+j^3)%n+1]++)); v
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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