Help me construcing finite field,

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SUMMARY

The discussion centers on constructing a finite field with q elements, specifically within the range of 10^9 to 10^10, using Mathematica without relying on any finite field packages. The user seeks guidance on how to implement this and clarifies the concept of a primitive root in this context. Key insights include the necessity of understanding finite field theory and the methods to identify primitive roots within these fields.

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Granit_niti
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Help me construcing finite field, please!

I need Construct a finite field with q Elements (10^9<q<10^10) and find
a primitive root. That should be done in mathematica but I should not use Package for Finite Fields.

Any idea how to solve this problem?
 
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What do you mean by primitive root here?
 

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