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The phrase "a fixed integer" is correct and usable in written English.
It can be used in mathematical or programming contexts where a specific, unchanging whole number is referenced.
Example: "In this algorithm, we need to define a fixed integer that will serve as the maximum limit for our calculations."
Alternatives: "a constant integer" or "a designated integer".
Exact(60)
Let d be a fixed integer bigger than 0, and let p be a fixed prime number and ( d, p ) = 1.
for a fixed integer.
Let be a fixed integer.
where n ≥ 2 is a fixed integer.
Let (mgeq1) be a fixed integer.
where k ≥ 1 is a fixed integer.
(ii) Let (b ge 2) denote a fixed integer.
Rassias introduced the following equality,, for a fixed integer.
For a fixed integer, we set with the restriction that.
( C 3 1 ) Let k ≥ 2 be a fixed integer.
for a fixed integer a with a ≠ 0, ± 1.
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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