Category: Number Theory

Class 9 English chapter 1 summary , Chapter How I Taught My Grandmother To Read,

book Kaveri, writer Sudha Murty

Associative Property

Distributive Property

Commutative Property

Identity Property

Zero Property

Closure Property

Introduction, natural number . Integers , rational number. All questions are given by PW

Nina memiliki 5 buah jeruk, lalu ibu membelimembelikan lagi 7 buah jeruk untuk nina, berapa jumlah jeruk yang nina miliki?

All questions are directly provide with pw

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give examples and give brief description below

is Irrational number because we can’t write in p/q form so is irrational no.

Nice, Number Theory lets go harder.

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NUMBER THEORY PROBLEM (Challenging)

Find all integers such that:

x^2 – 5x + 6 equiv 0 pmod{7}

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Solution

We solve this using Modular Arithmetic.

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Step 1: Work modulo 7

We test values of from to (since modulo 7 repeats).

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Step 2: Try values

Substitute into:

x^2 – 5x + 6 pmod{7}

:

:

:

:

:

:

:

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Step 3: Solutions modulo 7

x equiv 2 pmod{7}, quad x equiv 3 pmod{7}

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Final Answer

All integers of the form:

x = 7k + 2 quad text{or} quad x = 7k + 3

where is any integer

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