Solved

Factors of Positive Integers

Posted on 2014-04-17
4
263 Views
Last Modified: 2014-04-17
Sorry if this is a 6th-grade arithmetic question...

Can consecutive positive integers ever have a common factor greater than one?  Is there a formal proof?

Thanks and regards, ~Ray
0
Comment
Question by:Ray Paseur
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
  • 3
4 Comments
 
LVL 27

Expert Comment

by:d-glitch
ID: 40006808
No.  The proof is in modular arithmetic.
0
 
LVL 27

Accepted Solution

by:
d-glitch earned 500 total points
ID: 40006815
If P is a factor of N, then N=0 mod P.  
N+1 will always equal 0+1 mod P.

So if P is a factor of N, it can not be a factor of N+1.
0
 
LVL 27

Expert Comment

by:d-glitch
ID: 40006824
This is 1st year college Number Theory, not 6th grade arithmetic.
0
 
LVL 110

Author Closing Comment

by:Ray Paseur
ID: 40006829
Thanks.  I was going to test all the numbers but figured a proof would save time :-)
0

Featured Post

Database Solutions Engineer FAQs

In this series, we will discuss common questions received as a database Solutions Engineer at Percona. In this role, we speak with a wide array of MySQL and MongoDB users responsible for both extremely large and complex environments to smaller single-server environments.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

A Guide to the PMT, FV, IPMT and PPMT Functions In MS Excel we have the PMT, FV, IPMT and PPMT functions, which do a fantastic job for interest rate calculations.  But what if you don't have Excel ? This article is for programmers looking to re…
Have you ever thought of installing a power system that generates solar electricity to power your house? Some may say yes, while others may tell me no. But have you noticed that people around you are now considering installing such systems in their …
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
Suggested Courses
Course of the Month5 days, 3 hours left to enroll

635 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question