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The phrase "a unique solution to" is correct and usable in written English.
It can be used when discussing a specific problem or challenge that has only one effective answer or resolution.
Example: "In mathematics, we often seek a unique solution to complex equations that can be solved in only one way."
Alternatives: "an exclusive answer to" or "a singular resolution for".
Exact(60)
ReputationGuard is a unique solution to this exposure".
Docter Noel has a unique solution to the problem of a bee in your home.
Even so, the resulting computed Earth structure is not a unique solution to the problem.
Each virtual coin represents a unique solution to a complex cryptographic problem, aimed at preventing duplication and forgery.
For those with short memories, it's the season where "Bunny" Colvin comes up with a unique solution to the city's drugs problem – legalise everything.
By Theorem 3.2, there exists a unique solution to.
Then there exists a unique solution to (1.3).
then there exists a unique solution to problem T1.
Thus there exists a unique solution to (4.8).
then there exists a unique solution to the problem T0.
Under the assumptions (HA) to (HD), there exists a unique solution to the problem (P5).
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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