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

Home > Just Math
Diophantine Equation (Posted on 2013-05-14) Difficulty: 2 of 5
Solve in Integers

(5+3√2)m = (3+5√2)n

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution This should work Comment 1 of 1
The only solution is (m,n)=(0,0)

A^m = B^n
m*log(A) = n*log(B)
m/n = log(B)/log(A)

But log(5+3√2)/log(3+5√2) is clearly irrational so there are no integers m/n with n≠0.

A good approximation is 10117/9741 as supplied by
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfCALC.html#


  Posted by Jer on 2013-05-14 12:45:34
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 (11)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information