If a Prime Divides a Product...
نویسنده
چکیده
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. The Fundamental Theorem of Arithmetic states that every integer exceeding 1 can be written uniquely as a product of prime powers. There are may ways to prove this important theorem, and many applications. One of the most important consequences of unique factorization is in studying the Riemann zeta function, defined by
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