Tag: integers
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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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Playing with Primes
A Positional Notation of Integers and Rationals Based on Prime Factorization Let denote the primes, i.e. , The fundamental theorem of number theory, as proved e.g. in (Gauss, 1870), tells us that each integer can be represented as a unique product of primes. Let us represent integers as infinite lists we call prime vectors. Definition…
Michael Emmerich 