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"problem by itself" is a correct phrase in written English.
You can use it to refer to a singular issue or challenge that does not need any additional complications. For example, you might say, "This problem by itself is enough for us to worry about."
Exact(27)
"It's not the high school's problem by itself.
America cannot solve a global problem by itself.
American cash will not solve the problem by itself.
Either problem, by itself, makes nonsense of the whole claim.
Northern Ireland's devolved government will have to cope with this problem by itself.
"The difficulty is that no one institution can solve the problem by itself.
Similar(33)
Creating personal accounts will not solve Social Security's problems by itself.
The Race to the Top initiative won't solve this country's education problems by itself, but it is focusing attention on the right issues and moving them up the national agenda.
Swing also warned that solving the Syrian crisis would not solve Europe's migration problems by itself, since Syrians formed only half the numbers of those people moving towards the continent.
Some of the company officials said if the industry was to be left to solve the problems by itself, as they had urged, there had to be greater coordination and more uniform security standards.
Like a scientist or a playing child, PowerPlay (Schmidhuber, 2011) not only learns new skills to solve given problems, but also invents new interesting problems by itself.
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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