Can anyone please check my proof for this number theory problem?

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Homework Statement
Prove that ((a, b), b)=(a, b).
Relevant Equations
None.
Please view the picture of my work which I've uploaded.
 

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  • Number Theory.jpg
    Number Theory.jpg
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Looks good.
 
PeroK said:
Looks good.
Thank you.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

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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