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How about this sentence?

As an example, let us consider the cases a=3 and a=5.

Should it be

As examples?

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Both are possible, it depends on what you are trying to say

As examples

is correct, if a=3 and a=5 produces two different outcomes, each will be an example.

For example

can be used as a general introduction to what the examples will be.

For example, he not only runs but he can also skate.
As examples of his athletic prowess, be can also run and skate.

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