Equation: a^4 + b^4 ± k = c^2

 
 
a^4 \; + \; b^4 \; \pm \; k \; = \; c^2

where   k   is a small odd integer.

 

k = +3

2^4 \; + \; 3^4 \; + \; 3 \; = \; 10^2
116^4 \; + \; 825^4 + \; 3 \; = \; 680758^2

 

k = -7

2^4 \; + \; 2^4 \; - \; 7 \; = \; 5^2
14^4 \; + \; 80^4 \; - \; 7 \; = \; 6403^2

 

k = +7

3^4 \; + \; 3^4 \; + \; 7 \; = \; 13^2

 
 
Find other solutions where k is a small odd integer.

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 

Advertisements

About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s