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The phrase "a unique solution to this problem" is correct and usable in written English.
You can use it when discussing a specific issue that requires a distinct answer or approach.
Example: "After extensive research and analysis, we have identified a unique solution to this problem that will benefit all stakeholders involved."
Alternatives: "an exclusive answer to this issue" or "a singular resolution to this challenge".
Exact(5)
Computer science algorithms known as "shape matching" methods pose a unique solution to this problem by providing robust metrics for quantifying the similarity between pairs of arbitrarily complex structures.
A unique solution to this problem exists, since the objective function is strictly concave and the feasible set is convex.
Clay Blevins, president and principal owner of a company called Comfort Supply, has come up with what we think is a unique solution to this problem.
Moreover, to execute a parameter estimation task, first one needs to ensure the identifiability of the system, since if the number of unknown parameters is very large, it is often impossible to find a unique solution to this problem.
[ 14, 15] MLM offer a unique solution to this problem.
Similar(55)
where obviously is the unique solution to this problem.
Even so, the resulting computed Earth structure is not a unique solution to the problem.
then there exists a unique solution to the problem T0.
then there exists a unique solution to problem T1.
But Oliver proposed a very unique solution to the problem.
And so, is the unique solution to problem (2.10).
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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