Does c always divide b in number theory divisibility?

In summary, if a number is divisible by another number, then the product of that number and a third number will also be divisible by the first number. This knowledge can be applied to direct proofs in discrete math, which the person is currently learning and hopes to improve on in future exams.
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chimath35
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If a|b then ac=b; now does c always divide b as well?
 
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  • #2
chimath35 said:
If a|b then ac=b; now does c always divide b as well?

Of course it does.
 
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Thank you Dick; I did pass the exam I took by the way lol. I did not really get to study much as I was ill, but still did good enough compared to other class mates. I think I am growing A LOT mathematically. I am just now learning how to do direct proofs in discrete math so hopefully I will do better next exam, even though I am just auditing this course. I am learning how to become more of a mathematician I guess.
 

FAQ: Does c always divide b in number theory divisibility?

What is number theory divisibility?

Number theory divisibility is a branch of mathematics that studies the properties of integers and their divisibility relationships. It deals with determining whether one number is a factor of another number, and the patterns and rules that govern these relationships.

How do you determine if one number is divisible by another number?

To determine if one number is divisible by another number, you can use the division algorithm, which states that if a number is divided by another number, the remainder will be less than the divisor. In simpler terms, if the remainder is 0, then the two numbers are divisible.

What is the significance of prime numbers in number theory divisibility?

Prime numbers are incredibly important in number theory divisibility because they have only two factors, 1 and themselves. This means that they are only divisible by 1 and the number itself. Prime numbers help us understand the fundamental principles of divisibility and serve as building blocks for many mathematical concepts.

How is number theory divisibility used in cryptography?

Number theory divisibility plays a crucial role in cryptography, as it is used to create and decode secure codes. The security of a code depends on the difficulty of factoring large numbers, which is a key concept in number theory divisibility.

Can number theory divisibility be applied in real-world situations?

Yes, number theory divisibility has many practical applications in fields such as computer science, engineering, and finance. It is used in algorithms, coding, and data encryption, among other things. It also helps in finding common factors and simplifying fractions, which are useful in everyday life.

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