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

 Completing a triplet (Posted on 2018-02-24)
Given a^2+15226=c^2,

How many solutions (a,c) are there such that both numbers are positive integers?

Please comment upon the unexpected result.

 See The Solution Submitted by Ady TZIDON No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 generalized solution spoiler Comment 5 of 5 |

<o:p> </o:p>

since 15226= 2*7613 and 7613 is a prime number  -    let's solve for a general case:

(c+a) *(c-a) =2*p , p an odd prime

Solving for a & c there are 2 possible integer factorizations :

c+a =2p   c-a=1    or

c+a=p ,    c-a=2

In both sets of equation there are no   integer  solutions:

c+a and c-a  must be of the same parity, i.e. both odd or both even.

see my "spoiler" post

<

Edited on March 1, 2018, 4:15 am
 Posted by Ady TZIDON on 2018-02-28 05:28:07

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 (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information