Yes, you need static libraries to build a statically linked executable.
Static libraries are bundles of compiled objects. When you statically link with to library, it is effectively the same as taking the compilation results of that library, unpacking them in your current project, and using them as if they were your own objects.
Dynamic libraries are already linked. This means that some information like relocations have already been fixed up and thrown out.
Additionally, dynamic libraries must be compiled as position-independent code. This is not a restriction on static libraries, and results in a significant difference in performance on some common platforms (like x86).
There exist tools like ELF Statifier which attempt to bundle dynamically-linked libraries into a dynamically-linked executable, but it is very difficult to generate a correctly-working result in all circumstances.
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