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

Home > Just Math
Rational number's conversion (Posted on 2017-06-18) Difficulty: 4 of 5
Show that every positive rational number can be presented as a ratio of powers' sum in the following way:

(a2+b3)/ (c5+d7)

where a,b,c,d are positive integers, not necessarily distinct.

No Solution Yet Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Answer | Comment 4 of 5 |
Let the rational number be x/y. Let a=x^3*y^2, b=x^5*y^2, c=x*y, and d=x^2*y. Then, (a^2+b^3)/(c^5+d^7)=((x^3*y^2)^2+(x^5*y^2)^3)/((x*y)^5+(x^2*y)^7)=((x^6*y^4)+(x^15*y^6))/((x^5*y^5)+(x^14*y^7))=x/y.

  Posted by Math Man on 2017-06-20 07:36:16
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (3)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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