How to find all filenames with given extension

I need to find all .pem files on my system. Would the following do this?

sudo find / -type f -name *.pem

If not, how would I write a find command to find every file of the sort?

You’re on the right track — you just need to quote the pattern so that it gets interpreted by find and not by your shell:

sudo find / -type f -name '*.pem'

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