关于对算术基本定理证明的再认识

Re-thinking the Proof for the Fundamental Theorem of Arithmetic

算术基本定理是初等数论中一个非常重要的结论.在重新审视其证明的过程中,发现整除的性质,即“p为素数,a,b为整数.若p|ab,则p|a或p|b”,对于算术基本定理的证明起到了的关键作用,为此给出了该性质的两种不同证明,并揭示了如何去巧妙应用假设所蕴含的事实.

The fundamental theorem of arithmetic is a very important conclusion in elementary number theory.In the process of re-examining its proof,we found the property of divisibility,that is,“p is a prime number,a,b is an integer.If p|ab,then p|a or p|b”is the key role to the proof of the fundamentaltheorem.Finally,two different proofs of this property are given,and how to apply the facts contained inthe hypothesis is revealed.