The correct answer is: D. no article
The sentence “I’ve got a problem” is a common way to say that you have an issue or difficulty. In this case, the article “a” is not necessary because the word “problem” is not specific. It could be any kind of problem, so there is no need to identify it further.
The other options are incorrect because they all use articles. The article “an” is used before singular nouns that begin with a vowel sound. The article “the” is used before specific nouns. The article “no article” is used before general nouns.
In this case, the noun “problem” is general, so it does not need an article.