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

Home > Numbers
Algebra and Primes (Posted on 2013-12-25) Difficulty: 2 of 5
Find all triples (x, y, z) of positive integers such that x + y + z - 3xyz = p

where p is a prime greater than 3

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 4.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips PARITY et all Comment 3 of 3 |
Upon parity considerations, it was clear to me that the triplet must contain two even and one odd integer, otherwise p=even.

Although I have found few sample triplets, I did not perceive 
that there are two equal integers and one odd  neighbor.

After seeing Ch's output I realized that  the sums cover all prime numbers.

Enter SH, -  Saying - "give me a prime (over 3) and I will give you a triplet" 17=>6,6,5,  19=>6,6,7,  101=>34,34,33  etc

Nice puzzle - I have rated it 4.

  Posted by Ady TZIDON on 2013-12-25 14:40:51
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information