## 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)

math grad - Interest: Number theory
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### 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.

2. benvitalis says:

Yep