Diophantine equation : y^2 – p = 2^n, where p is a prime number

 
 
The diophantine equation     y^2 \; - \; p \; = \; 2^{n}

where   p   is a prime number   < 100
 

The only solutions to the diophantine equation     y^2 - 17 = 2^{n}
with   y > 0   are given by     (n, y)   =   (3, 5),   (5, 7),   (6, 9),   (9, 23)

The only solutions to the diophantine equation     y^2 - 41 = 2^{n}
with   y > 0   are given by     (n, y)   =   (3, 7),   (7, 13)

The only solutions to the diophantine equation     y^2 - 73 = 2^{n}
with   y > 0   are given by     (n, y)   =   (3, 9)

The only solutions to the diophantine equation     y^2 - 89 = 2^{n}
with   y > 0   are given by     (n, y)   =   (5, 11),   (13, 91)

The only solutions to the diophantine equation     y^2 - 97 = 2^{n}
with   y > 0   are given by     (n, y)   =   (7, 15)

 
Find solutions for   100 \; < \; p \; < \; 1000
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Advertisements

About benvitalis

math grad - Interest: Number theory
This entry was posted in Prime Numbers 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