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A333669
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The smallest nontrivial quadratic residue modulo n.
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1
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4, 3, 2, 4, 4, 4, 3, 4, 3, 2, 4, 4, 2, 4, 4, 4, 4, 3, 2, 4, 4, 3, 4, 4, 4, 4, 2, 4, 3, 2, 4, 4, 3, 4, 3, 4, 2, 4, 4, 4, 4, 2, 2, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 3, 2, 4, 4, 4, 3, 4, 4, 3, 4, 2, 4, 2, 3, 4, 4, 4, 3, 2, 4, 4, 2, 3, 4, 4, 4, 4, 4
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OFFSET
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5,1
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COMMENTS
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The values are 2, 3 and 4. If 2 is a square modulo n (see A057126) the value is 2. Otherwise, if 3 is a square modulo n (see A057125) the value is 3. If neither 2 or 3 are a square modulo n the value is 4.
Dedicated to Urs Meyer at the occasion of his 60th birthday.
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LINKS
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EXAMPLE
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The squares modulo 5 are 1 and 4, therefore a(5) = 4.
Modulo 6 the squares are 1, 3 and 4 which makes a(6) = 3.
a(7) = 2 since 2 == 3^2 (mod 7).
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MAPLE
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f:= proc(n) uses numtheory; if quadres(2, n)=1 then 2 elif quadres(3, n)=1 then 3 else 4 fi end proc:
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MATHEMATICA
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qrQ[m_, n_] := Module[{k}, Reduce[Mod[m-k^2, n]==0, k, Integers] =!= False];
a[n_] := If[qrQ[2, n], 2, If[qrQ[3, n], 3, 4]];
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PROG
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(PARI) a(n) = if(issquare(Mod(2, n)), 2, issquare(Mod(3, n)), 3, 4)
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CROSSREFS
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Cf. A057126 for the n where the value is 2 and A057125 for the n where the value is 3 if n was not in A057126.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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