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The phrase "the crucial problem" is correct and usable in written English.
It can be used to refer to an important problem or issue. For example, "The crucial problem facing the economy is how to balance the budget."
Exact(60)
But it's not the crucial problem.
This raises the crucial problem of research financing.
The crucial problem the study had to solve was the old causation-correlation problem.
This technique, which they called "wing warping," solved the crucial problem of roll.
The crucial problem the study had to solve was the old causation-correlation problem.
But the crucial problem is that for most people, this is misery.
The crucial problem in joining is wettability of such ceramics with copper.
In the interview today, Mr. Gaviria said the crucial problem in Peru was the intelligence chief, Mr. Montesinos.
The crucial problem of modern hearing aids is that they do not know which acoustical source an impaired listener would like to hear.
Other examples deal with the crucial problem of the validation of turbulence models in strongly interacting flows.
The crucial problem that interfacial failure in composite slab was prevented by using reinforcing bars across the interfaces.
More suggestions(18)
the important problem
the fundamental problem
the considerable problem
the vital problem
the instrumental problem
the crucial subject
the crucial dilemma
the crucial issue
the paramount problem
the substantial problem
the foundational problem
the crucial challenge
the crucial subjects
the key problem
the crucial challenging
the crucial challenges
the pivotal problem
the core problem
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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