A Diophantine Equation

by luimichael, Oct 25, 2007, 5:33 AM

Solving the following Diophantine Equation:
$ (a+1)(b+1)(c+1) = 2 (abc + 1)$ with $ a \le{}b \le{}c$.

Solution:
Step 1
$ (1+ \frac 1 a)(1+ \frac 1 b)(1+ \frac 1 c) = 2( 1+ \frac 1 {abc})$

$ \implies (1 +\frac 1 a)^3 > 2$
$ \implies a < \frac 1 {2^{\frac 1 3} - 1} = 3.78......$

Only need to consider the cases for a = 1, 2 or 3.

........
........
Problem Solved.

The solution set is {(2,5,8),(2,4,13),(3,3,7)}.
This post has been edited 1 time. Last edited by luimichael, Mar 5, 2017, 3:43 AM
Reason: Latex problem

Comment

0 Comments

a