All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
An Integer Root Problem (Posted on 2006-11-17) Difficulty: 2 of 5
Determine whether or not x²+7x-14(q²+1)=0 has any integer roots for integer q.

See The Solution Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution maybe? | Comment 1 of 2

I'm not sure if I'm doing this right, but I do not think there are any integer roots if q is an integer.

Solving using the quadratic formula means the roots are

-7 + sqrt[49 + 56(q^2+1)] / 2

For this to be an integer, sqrt[49 + 56(q^2+1)] must be an odd integer.  This simplifies to sqrt[7(15+8q^2)] so (15+8q^2) must be 0 mod 7, and then 8q^2 must be 6 mod 7.  However, there are no integer solutions for q for which this is true.

 


  Posted by tomarken on 2006-11-17 10:08:01
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information