Let N be the product of all the prime numbers less than 1000.
(a) Prove that every prime factor of N+1 is greater than 1000.
(b) Prove that every prime factor of N-1 is greater than 1000.
Thank you!
Quick math question!?
2016-06-06 4:11 am
回答 (1)
2016-06-06 4:14 am
✔ 最佳答案
N = p1 * p2 * .... * pn where p1, p2, etc are primes less than 1000.a) What's the remainder if you divide N+1 by any of those p's?
(This is the basis of a well-known proof by Euclid that there's no largest prime).
b) A little trickier, but I think you can still answer it by considering the remainder when you divide N-1 by any of the p's.
收錄日期: 2021-04-21 18:54:19
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20160605201142AATW057