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

Home > Numbers
Does it continue? 9: Diophantine friends (Posted on 2017-10-03) Difficulty: 3 of 5
Before trying the problem "note your opinion as to whether the observed pattern is known to continue, known not to continue, or not known at all."

Does each of the two Diophantine equations have just the exact same five positive solutions of x = {1,2,3,6,91}?

2x2(x2-1) = 3(y2-1)
x(x-1)/2 = 2z-1

No Solution Yet Submitted by Jer    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Thoughts, no proof. Comment 1 of 1

These look very much like Pell Equations and also elliptic curves.

A limited number of solutions is therefore expected, particularly with square x in the first equation, for which we could write 2a(a-1) = 3(y2-1). Note that we would then have (a-sqrta)= 2(2z-1) in the second equation.

Therefore I expect it is true.

Edited on October 4, 2017, 12:34 am
  Posted by broll on 2017-10-04 00:29:57

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 (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information