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

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The discussion revolves around a proof in number theory regarding divisibility. The original poster seeks clarification on a specific part of their proof, particularly the phrase "it follows that..." in the second sentence. A suggestion is made to rephrase it for clarity, stating "then c = ud, a = vd and (u,v)=1." Additionally, a reminder is given to future contributors to submit their work as text rather than as images or PDFs. The focus remains on improving the clarity and structure of the proof.
Math100
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Homework Statement
If c divides ab and (c, a)=d, then c divides db.
Relevant Equations
None.
This is my work.
 

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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.
 
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.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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