In the case of power residue being one, the relation between its index and modulus by an order of its base

Title: In the case of power residue being one, the relation between its index and modulus by an order of its base

Abstract: Fermat found his little theorem by examining Mersenne prime. This thesis discloses the numerical structure of Fermat’s observation on Mersenne prime and submits its expanded theorems, which differ from his little theorem. The structure is deduced from the more essential theorems which describe the relation between the index and the modulus of power residue being one.

2010 Mathematics Subject Classification: Primary 11A07; Secondary 11A41.
Key Words and Phrases: power residue,primes,Mersenne prime,Fermat’s little theorem.

Thesis pdf file: In the case of power residue being one, the relation between its index and modulus by an order of its base

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Published in Dec. 27, 2018