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# المحاضرة السابعة هياكل متقطعة

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.

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.

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.

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.

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.

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.

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.

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.

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 .