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In short: yes, Celeron processors are compatible with Pentium processors and LibreOffice should install just fine on a Celeron computer.

The system requirements for installing LibreOffice indeed say a Pentium-compatible processor is needed to install LibreOffice on Windows or Linux. A couple of brand names are mentioned as compatible: Pentium III (made by Intel) and Athlon (made by AMD).

Although processor specifications (clock speed, number of cores, 32 or 64) of new processors have changed pretty dramatically over the past years, the basic specification of what processors can do (the architecture) hasn't changed that much. There are two variants in nearly all consumer computers: x86 and x64. The latter architecture is newer and it is compatible to the former.

LibreOffice is built for x86 architectures (like Pentium, Athlon, Celeron are) and needs a reasonably recent processor to run smoothly. Pentium IIIs are from over a decade ago, so computers from recent years can run LibreOffice.