Materi Teori Bilangan

Belajar teori bilangan dari mulai dari materi yang dasar.

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Bilangan Prima

Bilangan prima adalah bilangan asli yang lebih dari $1$ yang tidak memiliki pembagi selain 1, seperti 2, 3, 5, 7 dan 11, sedangkan 4 dan 6 bukanalah bilangan prima sebab $4 = 2 \times 2$ dan $6 = 2 \times 3$ . Bilangan asli yang bukan bilangan prima kita sebut sebagai bilangan komposit.

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Oleh Ricky The Ising

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Algoritma Pembagian

Di dalam toples Andi, terdapat $97$ permen. Andi mengambil $5$ permen untuk dia berikan kepada $5$ temannya dimana masing-masing mendapatkan $1$ permen, sehingga permen Andi tersisa $92$ buah. Lalu Andi mengambil $5$ permen lagi untuk dibagikan kepada $5$ teman tadi dengan cara yang sama, berakibat permen di toples tersisa $87$ buah. Proses tersebut Andi lakukan secara terus-menerus sampai permen di toples kurang dari $5$ .

With Muh. Fadlan

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Persamaan Diophantine Linear

Persamaan Diophantine adalah sebuah persamaan suku banyak di mana variabel – variabel yang terlibat didefinisikan atas bilangan bulat. Nama Diophantine sendiri diambil dari seorang matematikawan bernama Diophantus, yang mempelajari tipe persamaan tersebut pada abad ke-3. Ia juga merupakan salah satu matematikawan yang mengenalkan simbol pada bidang aljabar. Bidang yang mempelajari masalah-masalah pada persamaan Diophantine saat ini dikenal dengan nama Diophantine analysis atau analisis Diophantine. Masalah yang dipelajari biasanya terkait dengan mencari eksistensi solusi, banyak solusi, atau cara untuk mendapatkan semua solusi.

Oleh Made Tantrawan

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Persamaan Diophantine Non Linear

Persamaan Diophantine non-linear adalah suatu persamaan Diophantine yang tidak linear atau dengan kata lain memiliki suku yang berderajat lebih dari 1. Secara umum, tidak ada teknik khusus yang dapat digunakan untuk mencari penyelesaian persamaan Diophantine non-linear. Pada artikel ini, akan dijelaskan beberapa persamaan Diophantine non-linear yang cukup terkenal dan telah diketahui penyelesaiannya, yakni Persamaan Phytagoras, Persamaan Pell, dll.

Oleh Made Tantrawan

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Teorema (kecil) Fermat

Teorema kecil Fermat merupakan salah satu teori penting yang mendasari berbagai macam teorema penting lain di dalam teori bilangan. Pada tulisan ini akan dijelaskan isi dan bukti dari teorema kecil Fermat beserta contoh pengaplikasiannya. Selain itu, salah satu perumuman dari teorema kecil Fermat juga akan dibahas.

Oleh Made Tantrawan

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Fungsi Floor

Untuk setiap bilangan real $x$ , selalu terdapat dengan tunggal bilangan bulat $n$ yang memenuhi $n \leq x < n+1$ . Bilangan ini kita sebut sebagai floor dari $x$ , yang disimbolkan dengan $n = \lfloor x \rfloor$ . Nilai $\lfloor x \rfloor$ pada dapat pula didefinisikan sebagai bilangan bulat terbesar yang tidak lebih dari $x$ .

Oleh Ricky The Ising

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KPK dan FPB

KPK (Kelipatan Persekutuan Terkecil) dan FPB (Faktor Tersekutuan Terbesar) merupakan salah satu hal yang dipelajari waktu kita menempuh sekolah dasar (SD). Pada saat SD, terkadang kita diminta untuk menghitung KPK dan FPB dari bilangan 24 dan 36. Soal seperti itu dulu bukan soal yang mudah namun sekarang dengan mudah kita bisa menjawab bahwa KPK dan FPB dari 24 dan 36 berturut-turut adalah 72 dan 12. Bagaimana menentukan KPK dan FPB dari

Oleh Ricky The Ising

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Order dari Suatu Bilangan

Diberikan bilangan asli relatif prima $a$ dan $n$. Apakah selalu terdapat bilangan asli $m$ sehingga $a^m \equiv 1 \mod n$? Handout ini akan menyelidiki sifat-sifat bilangan $m$ yang memenuhi kondisi tersebut.

Oleh Ricky The Ising

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