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#36 by Sean A. Irvine at Sun Mar 31 15:03:09 EDT 2024
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#35 by Sean A. Irvine at Sun Mar 31 15:02:26 EDT 2024
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| LINKS
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<a href="/index/Pri#primes_root">Index entries for primes by primitive root</a>
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| STATUS
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approved
editing
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#34 by Michael De Vlieger at Sat Dec 24 22:29:09 EST 2022
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#33 by Jianing Song at Sat Dec 24 16:13:00 EST 2022
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#32 by Jianing Song at Sat Dec 24 16:12:24 EST 2022
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#31 by Jianing Song at Sat Dec 24 11:24:03 EST 2022
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Discussion
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| Sat Dec 24
| 11:48
| Michel Marcus: add A163778 to xrefs ?
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#30 by Jianing Song at Sat Dec 24 11:23:35 EST 2022
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| COMMENTS
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Proof of equivalence: Writelet ord(a,k) be the multiplicative of a modulo k. First we notice that all terms are congruent to 3 modulo 4, since -4 is a quadratic residue modulo p if p == 1 (mod 4). If ord(4,p) = (p-1)/2. Note that (p-1)/2 is odd, so it is coprime to ord(-1,p) = 2. As a result, ord(-4,p) = ((p-1)/2) * 2 = p-1. Conversely, If ord(-4,p) = p-1, we must have ord(4,p) = (p-1)/2 by noting that ord(-4,p) <= lcm(2,ord(4,p)).
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| STATUS
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proposed
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#29 by Jon E. Schoenfield at Sat Dec 24 07:44:49 EST 2022
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#28 by Jon E. Schoenfield at Sat Dec 24 07:44:12 EST 2022
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| COMMENTS
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An odd prime p is a term if and only if p == 3 (mod 4), ) and that the multiplicative order of 2 modulo p is p-1 or (p-1)/2 (p-1 isif p == 3 (mod 8), (p-1)/2 if p == 7 (mod 8)).
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| STATUS
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proposed
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Discussion
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| Sat Dec 24
| 07:44
| Jon E. Schoenfield: Right?
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| 07:44
| Jon E. Schoenfield: “Write ord(a,k) be …”?
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#27 by Jianing Song at Sat Dec 24 05:53:33 EST 2022
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