Thesis

Unique factorization for ideals in cyclotomic integers and Fermat's Last Theorem for regular primes

The thesis goal is to prove unique prime factorization (UPF) for ideals in a cyclotomic integers in the most elementary and efficient way. This way it can later be formally verified. The reason is to help prepare a formal verification of Fermat's Last Theorem (FLT) for regular primes. This thesis could be used as blueprint to formally verifying UPF. Once formally verify, UPF will be added to the Archives of Formal Proofs (AFP). AFP is an electronic journal that serves as a library of proofs, examples, scientific developments, which have beed formally verified using the proof assistant Isabelle. Not only UPF will be added to the AFP but also all the math that took to formally verifing it. And this by itself is a major contribution to AFP. By having UPF in the AFP it will be easier to formally verify FLT for regular primes since the UPF for ideal is essential to the proof. Formally verifying FLT for regular primes can be a future thesis for another master student. Special thanks to Dr. Wayne Aitken, my Thesis Advisor. Thanks to his collaboration, guidance, patience,. and contribution, this thesis was made possible. Also thanks to my siblings and mother for supporting me through out this long journey. Keywords: Unique prime factorization, Fermat's Last Theorem for regular primes, Formal Verification, Isabelle, Cyclotomic fields.

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