What is the Proof of the Size of Divisors for Integers?

Thread starter cariad69
Start date Mar 9, 2012
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In summary, "Proof of size of divisors" is a mathematical concept used to determine the size or magnitude of the divisors of a given number. It is important because it helps in understanding the properties and factors of a given number, and can be applied to all types of numbers. The main difference between "Proof of size of divisors" and "Proof of existence of divisors" is that the former focuses on determining size while the latter only proves existence. Common methods used in "Proof of size of divisors" include prime factorization, Euclidean algorithm, and modular arithmetic.

Mar 9, 2012

cariad69

could anybody help me prove this

if a,b,c are integers and b doesn't equal zero

if a| b then |a| < | b|

in particular any divisors a of a positive divisor b must fall in the interval 1 < a <b

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Mar 9, 2012

morphism

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1) It's not a strict inequality

2) It follows from the definition of divisor

Mar 9, 2012

HallsofIvy

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Homework Helper

If a|b then b= a*?

1. What is "Proof of size of divisors"?

Proof of size of divisors is a mathematical concept used to determine the size or magnitude of the divisors of a given number. It involves using various methods and techniques to prove the existence and properties of divisors.

2. Why is "Proof of size of divisors" important?

"Proof of size of divisors" is important because it helps in understanding the properties and factors of a given number. This is particularly useful in number theory, cryptography, and other branches of mathematics.

3. How is "Proof of size of divisors" different from "Proof of existence of divisors"?

The main difference between the two is that "Proof of size of divisors" focuses on determining the size or magnitude of the divisors, while "Proof of existence of divisors" only proves the existence of divisors. In other words, "Proof of existence of divisors" is a subset of "Proof of size of divisors."

4. What are some common methods used in "Proof of size of divisors"?

Some common methods used in "Proof of size of divisors" include prime factorization, Euclidean algorithm, and modular arithmetic. These methods help in determining the size and properties of divisors in a given number.

5. Can "Proof of size of divisors" be applied to all types of numbers?

Yes, "Proof of size of divisors" can be applied to all types of numbers, including integers, real numbers, and complex numbers. However, the specific methods and techniques used may vary depending on the type of number being analyzed.