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الكلية كلية تكنولوجيا المعلومات     القسم قسم البرامجيات     المرحلة 1
أستاذ المادة فريال جاسم عبدالرزاق الحميداوي       21/05/2017 21:56:28
Number theory is about integers and their properties.

We will start with the basic principles of

divisibility,
greatest common divisors,
least common multiples, and
modular arithmetic

and look at some relevant algorithms.
If a and b are integers with a ? 0, we say that a divides b if there is an integer c so that b = ac.

When a divides b we say that a is a factor of b and that b is a multiple of a.

The notation a | b means that a divides b.

We write a X b when a does not divide b
(see book for correct symbol).
For integers a, b, and c it is true that

if a | b and a | c, then a | (b + c)
Example: 3 | 6 and 3 | 9, so 3 | 15.

if a | b, then a | bc for all integers c
Example: 5 | 10, so 5 | 20, 5 | 30, 5 | 40, …

if a | b and b | c, then a | c
Example: 4 | 8 and 8 | 24, so 4 | 24.


Number theory is about integers and their properties.

We will start with the basic principles of

divisibility,
greatest common divisors,
least common multiples, and
modular arithmetic

and look at some relevant algorithms.
If a and b are integers with a ? 0, we say that a divides b if there is an integer c so that b = ac.

When a divides b we say that a is a factor of b and that b is a multiple of a.

The notation a | b means that a divides b.

We write a X b when a does not divide b
(see book for correct symbol).
For integers a, b, and c it is true that

if a | b and a | c, then a | (b + c)
Example: 3 | 6 and 3 | 9, so 3 | 15.

if a | b, then a | bc for all integers c
Example: 5 | 10, so 5 | 20, 5 | 30, 5 | 40, …

if a | b and b | c, then a | c
Example: 4 | 8 and 8 | 24, so 4 | 24.


Number theory is about integers and their properties.

We will start with the basic principles of

divisibility,
greatest common divisors,
least common multiples, and
modular arithmetic

and look at some relevant algorithms.
If a and b are integers with a ? 0, we say that a divides b if there is an integer c so that b = ac.

When a divides b we say that a is a factor of b and that b is a multiple of a.

The notation a | b means that a divides b.

We write a X b when a does not divide b
(see book for correct symbol).
For integers a, b, and c it is true that

if a | b and a | c, then a | (b + c)
Example: 3 | 6 and 3 | 9, so 3 | 15.

if a | b, then a | bc for all integers c
Example: 5 | 10, so 5 | 20, 5 | 30, 5 | 40, …

if a | b and b | c, then a | c
Example: 4 | 8 and 8 | 24, so 4 | 24.
Number theory is about integers and their properties.

We will start with the basic principles of

divisibility,
greatest common divisors,
least common multiples, and
modular arithmetic

and look at some relevant algorithms.
If a and b are integers with a ? 0, we say that a divides b if there is an integer c so that b = ac.

When a divides b we say that a is a factor of b and that b is a multiple of a.

The notation a | b means that a divides b.

We write a X b when a does not divide b
(see book for correct symbol).
For integers a, b, and c it is true that

if a | b and a | c, then a | (b + c)
Example: 3 | 6 and 3 | 9, so 3 | 15.

if a | b, then a | bc for all integers c
Example: 5 | 10, so 5 | 20, 5 | 30, 5 | 40, …

if a | b and b | c, then a | c
Example: 4 | 8 and 8 | 24, so 4 | 24.


Number theory is about integers and their properties.

We will start with the basic principles of

divisibility,
greatest common divisors,
least common multiples, and
modular arithmetic

and look at some relevant algorithms.
If a and b are integers with a ? 0, we say that a divides b if there is an integer c so that b = ac.

When a divides b we say that a is a factor of b and that b is a multiple of a.

The notation a | b means that a divides b.

We write a X b when a does not divide b
(see book for correct symbol).
For integers a, b, and c it is true that

if a | b and a | c, then a | (b + c)
Example: 3 | 6 and 3 | 9, so 3 | 15.

if a | b, then a | bc for all integers c
Example: 5 | 10, so 5 | 20, 5 | 30, 5 | 40, …

if a | b and b | c, then a | c
Example: 4 | 8 and 8 | 24, so 4 | 24.


Number theory is about integers and their properties.

We will start with the basic principles of

divisibility,
greatest common divisors,
least common multiples, and
modular arithmetic

and look at some relevant algorithms.
If a and b are integers with a ? 0, we say that a divides b if there is an integer c so that b = ac.

When a divides b we say that a is a factor of b and that b is a multiple of a.

The notation a | b means that a divides b.

We write a X b when a does not divide b
(see book for correct symbol).
For integers a, b, and c it is true that

if a | b and a | c, then a | (b + c)
Example: 3 | 6 and 3 | 9, so 3 | 15.

if a | b, then a | bc for all integers c
Example: 5 | 10, so 5 | 20, 5 | 30, 5 | 40, …

if a | b and b | c, then a | c
Example: 4 | 8 and 8 | 24, so 4 | 24.


Number theory is about integers and their properties.

We will start with the basic principles of

divisibility,
greatest common divisors,
least common multiples, and
modular arithmetic

and look at some relevant algorithms.
If a and b are integers with a ? 0, we say that a divides b if there is an integer c so that b = ac.

When a divides b we say that a is a factor of b and that b is a multiple of a.

The notation a | b means that a divides b.

We write a X b when a does not divide b
(see book for correct symbol).
For integers a, b, and c it is true that

if a | b and a | c, then a | (b + c)
Example: 3 | 6 and 3 | 9, so 3 | 15.

if a | b, then a | bc for all integers c
Example: 5 | 10, so 5 | 20, 5 | 30, 5 | 40, …

if a | b and b | c, then a | c
Example: 4 | 8 and 8 | 24, so 4 | 24.


Number theory is about integers and their properties.

We will start with the basic principles of

divisibility,
greatest common divisors,
least common multiples, and
modular arithmetic

and look at some relevant algorithms.
If a and b are integers with a ? 0, we say that a divides b if there is an integer c so that b = ac.

When a divides b we say that a is a factor of b and that b is a multiple of a.

The notation a | b means that a divides b.

We write a X b when a does not divide b
(see book for correct symbol).
For integers a, b, and c it is true that

if a | b and a | c, then a | (b + c)
Example: 3 | 6 and 3 | 9, so 3 | 15.

if a | b, then a | bc for all integers c
Example: 5 | 10, so 5 | 20, 5 | 30, 5 | 40, …

if a | b and b | c, then a | c
Example: 4 | 8 and 8 | 24, so 4 | 24.






المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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