publications - Co-authorship just because a Professor provides me the employment?

I am a postdoc at a European University. However, I am planning to quit my postdoc in a month or so since the research environment and the city life is not to me liking.

Also, I work with a Professor who is very polite, but also very busy with meetings. My salary comes from the project he administers, so he is the boss of the organization and the project.

For the past four months I have been working on a problem day and night including weekends as I found the problem very interesting and challenging. The theoretical part of the work is complete. It is a "complete" solution. He had NO contribution at all in this. Not even a single email exchange. He is too busy with meetings all the time. He is in the department twice a week for two to three hours at a time. I am also managing his master student as he has no time.

He is definitely polite and nice though, but I have not received any input from him other than giving me printed research papers. But he always asked me to give him the PDFs of lengthy derivations which I did. But I am dealing with analytical/numerical Navier-Stokes equation and its variations, so you can imagine how much terse that is. He has the entire theory now with him from my work. He may have been a good researcher in the past but no contribution to this work. And he had no proper publication in the work that I am doing so I am not sure how much he can contribute in writing the paper.

Now remains the numerical part which I believe I can do in next 2/3 weeks. And I have the ability to write the paper by myself when I have the numerical solution.

I talked to him and asked if I can work for him based in another city. He said if it is a week visit, that is fine, but not otherwise. He said it clearly that "I will not pay you to work somewhere else."

I still have a cordial relationship with him. No worries on that part. So, I am going to leave the place and the position in a month or two for sure.

So, he gains co-authorship just because he has the authority to provide employment? What should I do? Please help. I could have continued to live in the city though it was little boring for me, provided I was able to get inputs from my collaborator, or if he had given me necessary freedom to collaborate with other researchers, which he hasn't.

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Update 10th June, I have resigned now. This problem has evolved into a new stage. Please post your replies there:

Gifting co-authorship if the topic of research was suggested by my boss?

and

Acknowledgment of funding and adding an affiliation in exchange of permission to use experimental data?