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primary topic: KARAKTERISTIK BILANGAN CARMICHAEL

KARAKTERISTIK BILANGAN CARMICHAEL
type: Article
abstract: Berdasarkan teorema Fermat yang mengatakan bahwa jika p prima dan a bukan kelipatan p, maka ap−1 ≡ 1 (mod p), maka teorema ini memberikan kemungkinan cara untuk mendeteksi bilangan prima atau lebih tepatnya bukan bilangan prima, yaitu jika a relative prima dengan n, an – 1 tidak kongruen dengan 1, maka dengan teorema Fermat tersebut n bukan bilangan prima. Banyak bilangan komposit yang dapat dideteksi dengan menggunakan teorema ini. Untuk bilangan bulat a > 1, himpunan F(a) menyatakan himpunan bilangan positif n yang memenuhi an−1 ≡ 1 mod n. Dengan teorema Fermat, F(a) memuat semua bilangan prima yang bukan pembagi dari a. Jika n ∈ F(a), maka gcd(a,n) = 1, hal ini karena gcd(an−1, n) = 1. Jugna karena an ≡ a mod n;kebaliakn pernyataan tersebut benar, yang menyatakan bahwa a and n relative prima. Suatu bilangan komposit n yang termuat di F(a) disebut pseudoprima-a, atau pseudoprima dengan basis a. Suatu bilangan n yang pseudoprima-a untuk semua a yang relative prima dengan n dinamakan bilangan Carmichael . Bilangan dengan bentuk (6m + 1)(12m + 1)(18m + 1) dengan tiga factor semuanya prima merupakan contoh bilangan Carmichael. Kata Kunci : Bilangan Carmichael , bilangan bulat positif , bilangan prima, bilangan komposit, relative prima, pseudoprima. Recall that Fermat’s “little theorem” says that if p is prime and a is not a multiple of p, then ap−1 ≡ 1 (mod p). This theorem gives a possible way to detect primes, or more exactly, non-primes: if for a certain a coprime to n, an−1 is not congruent to 1 mod n, then, by the theorem, n is not prime. A lot of composite numbers can indeed be detected by this test, but there are some that evade it. For a fixed a > 1, we write F(a) for the set of positive integers n satisfying an−1 ≡ 1 mod n. By Fermat’s theorem, F(a) includes all primes that are not divisors of a. If n ∈ F(a), then gcd(a,n) = 1, since, clearly, gcd(an−1, n) = 1. Also, an ≡ a mod n;the reverse implication is true provided that a and n are coprime. A composite n…
date: 2015-09-02
status: published
author list: authors
type: EPrint
type: OtherEPrint
is part of: repository
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fakultas MIPA
type: Organization

1017031021 Devi Purnama sari
type: Person
given name: 1017031021
family name: Devi Purnama sari

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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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KARAKTERISTIK BILANGAN CARMICHAEL (Other)
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HTML Summary of #13978 KARAKTERISTIK BILANGAN CARMICHAEL
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primary topic: KARAKTERISTIK BILANGAN CARMICHAEL

QA Mathematics
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