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A373748
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Triangle read by rows: T(n, k) is k if k is a quadratic residue modulo n, otherwise is -k and is a quadratic nonresidue modulo n. T(0, 0) = 0 by convention.
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5
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0, 0, 1, 0, 1, 2, 0, 1, -2, 3, 0, 1, -2, -3, 4, 0, 1, -2, -3, 4, 5, 0, 1, -2, 3, 4, -5, 6, 0, 1, 2, -3, 4, -5, -6, 7, 0, 1, -2, -3, 4, -5, -6, -7, 8, 0, 1, -2, -3, 4, -5, -6, 7, -8, 9, 0, 1, -2, -3, 4, 5, 6, -7, -8, 9, 10, 0, 1, -2, 3, 4, 5, -6, -7, -8, 9, -10, 11, 0, 1, -2, -3, 4, -5, -6, -7, -8, 9, -10, -11, 12
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,6
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LINKS
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EXAMPLE
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Triangle starts:
[0] [0]
[1] [0, 1]
[2] [0, 1, 2]
[3] [0, 1, -2, 3]
[4] [0, 1, -2, -3, 4]
[5] [0, 1, -2, -3, 4, 5]
[6] [0, 1, -2, 3, 4, -5, 6]
[7] [0, 1, 2, -3, 4, -5, -6, 7]
[8] [0, 1, -2, -3, 4, -5, -6, -7, 8]
[9] [0, 1, -2, -3, 4, -5, -6, 7, -8, 9]
[10] [0, 1, -2, -3, 4, 5, 6, -7, -8, 9, 10]
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MAPLE
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QR := (a, n) -> ifelse(n = 0, 1, NumberTheory:-QuadraticResidue(a, n)):
for n from 0 to 10 do seq(a*QR(a, n), a = 0..n) od;
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MATHEMATICA
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qr[n_] := qr[n] = Join[Table[PowerMod[k, 2, n], {k, 0, Floor[n/2]}], {n}];
T[0, 0] := 0; T[n_, k_] := If[MemberQ[qr[n], k], k, -k];
Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten
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PROG
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(SageMath)
def Trow(n):
q = set(mod(a * a, n) for a in range(n // 2 + 1)).union({n})
return [k if k in q else -k for k in range(n + 1)]
for n in range(11): print(Trow(n))
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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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