If a prime divides a product
Steven J. Miller, Cesar E. Silva
TL;DR
This paper discusses common pitfalls in proof-based mathematics, specifically highlighting how assumptions about prime divisibility can lead to errors in proofs involving factorization and gcd.
Contribution
It clarifies a specific example of subtle assumptions in proofs related to primes, gcd, and unique factorization, emphasizing careful logical reasoning.
Findings
Identifies common logical errors in proofs involving primes and divisibility
Highlights the importance of rigorous proof techniques in number theory
Provides insights into avoiding assumptions in mathematical proofs
Abstract
One of the greatest difficulties encountered by all in their first proof intensive class is subtly assuming an unproven fact in a proof. The purpose of this note is to describe a specific instance where this can occur, namely in results related to unique factorization and the concept of the greatest common divisor.
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Taxonomy
TopicsRings, Modules, and Algebras · Algebraic Geometry and Number Theory · History and Theory of Mathematics