Solved

# Factors of Positive Integers

Posted on 2014-04-17
244 Views
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
Question by:Ray Paseur
• 3

LVL 27

Expert Comment

No.  The proof is in modular arithmetic.
0

LVL 27

Accepted Solution

d-glitch earned 500 total points
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

This is 1st year college Number Theory, not 6th grade arithmetic.
0

LVL 108

Author Closing Comment

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

## Featured Post

### Suggested Solutions

Suppose you use Uber application as a rider and you request a ride to go from one place to another. Your driver just arrived at the parking lot of your place. The only thing you know about the ride is the license plate number. How do you find your U…
The greatest common divisor (gcd) of two positive integers is their largest common divisor. Let's consider two numbers 12 and 20. The divisors of 12 are 1, 2, 3, 4, 6, 12 The divisors of 20 are 1, 2, 4, 5, 10 20 The highest number among the c…
It is a freely distributed piece of software for such tasks as photo retouching, image composition and image authoring. It works on many operating systems, in many languages.
You have products, that come in variants and want to set different prices for them? Watch this micro tutorial that describes how to configure prices for Magento super attributes. Assigning simple products to configurable: We assigned simple products…