a + b + c + a*b + b*c + c*a = a*b*c + 1

 
 

Find all triples   ( \, a, \; b, \; c \, )   of positive integers such that

a \; \leq \; b \; \leq \; c ,     and

a \; + \; b \; + \; c + \; a \, b \; + b \, c \; + \; c \, a \; = \; a \, b \, c \; + \; 1

 
 
 
 

Solution:

(a, b, c)   =   (2, 4, 13),   (2, 5, 8),   (3, 3, 7)
 

 
 
 
 
 
 
 
 
 
 
 
 
 

Advertisements

About benvitalis

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

2 Responses to a + b + c + a*b + b*c + c*a = a*b*c + 1

  1. Paul says:

    Format {a, b, c}
    {2, 4, 13}
    {2, 5, 8}
    {3, 3, 7}

    Paul.

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