Would you please correct this letter for me? Thank you in advance

I want to have a very respectful letter to send to a professor. What is your opinion about the following message? Is it polite? or does it need to change in some parts?

Dear Professor .......
Around two months ago, I have communicated with you for over 10 days and during that time and through your guidance, I could correct xxxxx equation which had been miscalculated by myself earlier. Now I have written a paper and I want to submit it. xxxxx equation is used as some part of basic calculation in the paper. In the section acknowledgement, if you accept, I want to appreciate you for your advice but before that I'd like to inform you about this task. Please tell me whether you agree or not.
Best regard
the formal name will be replaced here

Dear Professor..

You were recently kind enough to help me work through a problem involving xxx equation which had been causing me difficulties.  I have now writtenn a paper which I intend to submit for publication in which this equation features. With your permission, I would like to acknowledge your assistance.  If you are agreeable to this, please let me know.

With best regards and appreciation for your help