Proving the Property: Relatively Prime Factors and Division

Thread starter abcd8989
Start date Oct 23, 2010
Tags

Property

In summary, the type of evidence needed to prove a property will depend on its nature and characteristics. The steps for proving a property involve defining it, collecting data, analyzing and interpreting it, and considering potential limitations. To ensure validity and reliability, careful design, appropriate controls, and peer review are important. While it is not possible to prove a property with absolute certainty, strong evidence can increase confidence in its truth. To effectively communicate a proof, clear explanations, consideration of the audience, and visual aids can be helpful.

Oct 23, 2010

abcd8989

If pq=ab where p, b are relatively prime, p must be a factor of a and b must be a factor of q.

Physics news on Phys.org

Oct 24, 2010

shoplifter

well, since ab = pq, p divides ab. but (p, b) = 1 and so p must divide a [this is obvious, trust me. if you don't see it, break them up into prime factors and deal with them case by case]. the other direction is symmetric.

1. How do I determine which type of evidence is needed to prove a property?

The type of evidence needed to prove a property will depend on the nature of the property itself. Some properties may require experimental data and measurements, while others may require mathematical proofs or logical arguments. It is important to carefully consider the specific property and its characteristics before determining the appropriate type of evidence.

2. What steps should I follow to prove a property?

The specific steps for proving a property will vary depending on the type of evidence required. Generally, the process will involve carefully defining the property, collecting relevant data or information, analyzing and interpreting the data, and drawing conclusions based on the evidence. It is also important to consider potential limitations or alternative explanations for the property.

3. How can I ensure the validity and reliability of my evidence?

To ensure the validity and reliability of your evidence, it is important to carefully design your experiments or studies, use appropriate controls, and accurately record and analyze your data. It is also helpful to have your evidence reviewed by other experts in the field to identify any potential flaws or biases.

4. Can a property be proven with absolute certainty?

In science, it is generally not possible to prove a property with absolute certainty. This is because new evidence or discoveries could potentially disprove or modify the property in the future. However, strong and consistent evidence can greatly support the validity of a property and increase our confidence in its truth.

5. How can I communicate my proof to others in a clear and effective way?

To effectively communicate your proof to others, it is important to clearly define and explain the property being proven, provide a thorough and logical explanation of the evidence and analysis used, and consider the audience and their level of understanding. Visual aids, such as graphs or diagrams, can also be helpful in presenting the evidence in a clear and concise manner.