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A229710
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Least m of maximal order mod n such that m is a sum of two squares.
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2
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2, 5, 5, 5, 2, 13, 2, 5, 2, 5, 2, 5, 5, 5, 2, 13, 2, 13, 5, 5, 2, 37, 2, 5, 2, 13, 13, 5, 2, 5, 2, 5, 2, 13, 2, 13, 13, 5, 5, 13, 2, 5, 5, 5, 5, 13, 5, 37, 2, 5, 2, 5, 2, 37, 2, 13, 2, 13, 2, 5, 2, 5, 2, 5, 2, 17, 13, 5, 5, 5, 2, 13, 2, 37, 29, 13, 2, 13, 2, 5
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OFFSET
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5,1
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COMMENTS
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The sequence is undefined at n=4, as all the primitive roots are congruent to 3 mod 4.
Terms are not necessarily prime. For example, a(109) = 10.
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LINKS
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EXAMPLE
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The integer 5 = 2^2 + 1^2 has order 2 mod 12, the maximum, so a(12) = 5.
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PROG
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(Sage) def A229710(n) : m = Integers(n).unit_group_exponent(); return 0 if n==1 else next(i for i in PositiveIntegers() if mod(i, n).is_unit() and mod(i, n).multiplicative_order() == m and all(p%4 != 3 or e%2==0 for (p, e) in factor(i)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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