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.
 

Thread 'Does this series converge uniformly?'

First, I tried to show that ##f_n## converges uniformly on ##[0,2\pi]##, which is true since ##f_n \rightarrow 0## for ##n \rightarrow \infty## and ##\sigma_n=\mathrm{sup}\left| \frac{\sin\left(\frac{n^2}{n+\frac 15}x\right)}{n^{x^2-3x+3}} \right| \leq \frac{1}{|n^{x^2-3x+3}|} \leq \frac{1}{n^{\frac 34}}\rightarrow 0##. I can't use neither Leibnitz's test nor Abel's test. For Dirichlet's test I would need to show, that ##\sin\left(\frac{n^2}{n+\frac 15}x \right)## has partialy bounded sums...
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