Tag: Fundamental Theorem of Arithmetics
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On Prime Vectors and Unique Factorization of Rationals
Michael Emmerich, January 9, 2025 In this essay, we use the theory of prime vectors (see [1]) to provide an alternative proof of the unique factorization of integers into prime factors: Unlike earlier proofs [4], notably its first proof by Carl Friedrich Gauss [3], this extends unique factorization to rational numbers, and we also establish…
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Fundamental Theorem of Arithmetics: A proof from first principles
The Fundamental Theorem of Arithmetic:A Proof from Elementary Principles Michael Emmerich, December 7th, 2024 The Fundamental Theorem of Arithmetic states that every integer greater than 1 can be uniquely represented as a product of prime numbers, apart from the order of the factors. This essay aims to prove the theorem rigorously from elementary principles, i.e.,…
Michael Emmerich 