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The phrase "are two basic problems" is correct and usable in written English.
It can be used when introducing or discussing two fundamental issues or challenges in a particular context.
Example: "In our analysis of the situation, we found that there are two basic problems that need to be addressed: lack of communication and insufficient resources."
Alternatives: "there exist two primary issues" or "two main challenges are present".
Exact(9)
"There are two basic problems they have to prepare for.
Outside of Wall Street, there are two basic problems.
There are two basic problems with my old beliefs.
But there are two basic problems with this contention.
There are two basic problems with consuming caffeine when cortisol production is high.
There are two basic problems here.
Similar(51)
There are three basic problems with stop and search.
There are three basic problems - one is it is actually really difficult to discover new antibiotics; it is not a trivial exercise.
There are three basic problems in dealing with the stability of discrete switched systems: (1) Find the stability or controller design of switched systems under an arbitrary switching signal [3, 4, 8, 9, 13]; (2) Identify the useful stabilizing switching signal for switched systems [14]; (3) Construct the stabilizing switching signal for switched systems [6, 7].
There are three basic problems creating orphan elephants at an escalating rate: exploding human populations across Africa (as in other impoverished places) have eliminated elephants from many countries.
There are three basic problems: one, maintaining a productive caste ratio between the two groups, two, ensuring the steady replacement of foragers as they die, and three, rapidly boosting the forager population during nectar flows.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com