I have found this this article on Chinese Wikipedia that shows a table with the columns 省会 (provincial capital) and 省份 (province) (see screenshot below).
The table above contains the information that I'm looking for, but to ensure the most reliable information, I would like to read it from a public institution in the People's Republic of China (perhaps, there is a document or website under the domain www.gov.cn that list such information.)
Additional information
I found this document published on 2017 in www.gov.cn that states the following:
截至2016年底,全国共有省级行政区划单位34个(其中直辖市4个、省23个、自治区5个、特别行政区2个),地级行政区划单位334个(其中地级市293个、地区8个,自治州30个、盟3个),……
The English translation is shown below:
By the end of 2016, there were 34 provincial-level administrative division units across the country (including 4 municipalities directly under the Central Government, 23 provinces, 5 autonomous regions, and 2 special administrative regions), and 334 prefecture-level administrative division units (including 293 prefecture-level cities, 8 regions, 30 autonomous prefectures, and 3 unions).,……
So, according to the People's Republic of China, China has 34 provincial-level administrative divions, among which:
- 4 municipalities directly under the Central Government (in Chinese, 直辖市4个)
- 23 provinces (in Chinese, 省23个)
- 5 autonomous regions (in Chinese, 自治区5个)
- 2 special administrative regions (in Chinese, 特别行政区2个)
Therefore, the list of the accepted answer should have 34 entries. I suppose that every province has a capital. If that's not the case, the list should list the capital for those provinces that have it.