## Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square

The set   $\{ \, a, \; b, \; c, \; d, \; e \, \}$   has the property that the product of any two of them plus one is the square of a rational number.

$a \,b + 1$   ……….   $b \,c + 1$   ……….   $c \,d + 1$   ……….   $d \,e + 1$
$a \,c + 1$   ……….   $b \,d + 1$   ……….   $c \,e + 1$
$a \,d + 1$   ……….   $b \,e + 1$
$a \,e + 1$

are all perfect squares

where   $a = 2$

## About benvitalis

math grad - Interest: Number theory
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