perplexus.info :: Just Math : My favorite numbers IV

My favorite numbers IV (Posted on 2010-05-08)

Determine all possible quadruplet(s) (A, B, C, D) of positive integers, with A ≥ C, that satisfy this system of equations:

A/B = C-D, and:

C/D = A-B

Prove that these are the only quadruplet(s) that exist.

Submitted by K Sengupta

Rating: 3.0000 (2 votes)

Solution: (Hide)

There are only three solutions:
(4,2,4,2) and (6,2,4,1) and (6,3,3,1)
For an explanation, refer to the solution submitted by Steve Herman in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
quadruplets and proof	Steve Herman	2010-05-09 11:10:14
Three distinct answers	Brian Smith	2010-05-09 11:09:36
quadruplet	Dej Mar	2010-05-08 20:21:56

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info