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The sentence "The problem has been solved" is correct and usable in written English
You could use it when referring to a problem that has been successfully solved. For example: "The computer issue we've been having has been solved – it turns out the cables weren't plugged in correctly".
Exact(53)
The problem has been solved using both heuristic and exact methods.
The problem has been solved by both Berger's approach and the more rigorous von Kármán approach.
The problem has been solved using a new hybrid evolutionary algorithm.
The problem has been solved for both low and high frequencies for small coupling parameter.
The problem has been solved numerically by using the exterior SUMT in which the Powell unconstrained minimization technique improved by Sargent with the parabolic interpolation method of one-dimensional minimization, is employed.
The problem has been solved by considering concrete mechanics described by Eqs. 5 and 6.
Similar(7)
How else could the problem have been solved?
"I thought this was not possible, that the problem had been solved by the judge," Mr. Sanchez said.
An Israeli television report tonight claimed the problem had been solved, but officials said that was premature.
After the problem had been solved, Fonda stood, with the aid of a cane, to show me how her recovery was progressing.
By the time the problem had been solved only 12 laps remained and Hamilton's hopes of a podium finish were long gone.
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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