Can anyone please check my work of this proof? (Number Theory)

In summary, a proof in number theory is a rigorous way to demonstrate the validity of a mathematical statement or theorem. The best way to check the correctness of a proof is to have someone else review it, and examples can be useful in understanding but should not be relied upon solely. Common mistakes to avoid include circular reasoning, incorrect assumptions, and unclear explanations. To improve proof-writing skills, practice, studying other proofs, seeking feedback, and continuous revisions are recommended.
  • #1
Math100
756
202
Homework Statement
If c divides ab and (c, a)=d, then c divides db.
Relevant Equations
None.
This is my work.
 

Attachments

  • Proof (3).pdf
    1.1 MB · Views: 89
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  • #2
I'm not clear on your "it follows that..." in the 2nd sentence. Better to say "then c = ud, a = vd and (u,v)=1." and work from there.
 
  • #3
Math100 said:
Homework Statement:: If c divides ab and (c, a)=d, then c divides db.
Relevant Equations:: None.

This is my work.
@Math100, in future threads, please post your work as text, rather than as a photo in a pdf file.
 
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Likes PhDeezNutz

1. What is the purpose of a proof in number theory?

A proof in number theory is used to demonstrate the validity of a mathematical statement or theorem. It provides a logical and rigorous explanation for why a certain statement is true.

2. How do I know if my proof is correct?

In order for a proof to be considered correct, it must follow a logical and coherent structure, use valid mathematical reasoning, and provide evidence for each step. It is also important to check for any errors or inconsistencies in the proof.

3. Can I use any mathematical notation or symbols in my proof?

Yes, mathematical notation and symbols are commonly used in proofs in number theory. It is important to use them correctly and consistently throughout the proof.

4. Is it necessary to include all steps in a proof?

Yes, it is important to include all steps in a proof in order to provide a clear and complete explanation of the reasoning behind the statement. Omitting steps can make the proof incomplete or confusing.

5. Can someone else check my work of a proof in number theory?

Yes, it is always helpful to have someone else review your work and provide feedback. This can help identify any errors or areas that may need further clarification. It is also a good practice to seek feedback from experts in the field of number theory.

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