Set {3,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
 

Here we have   a = 3

 
We obtain 2 families of solutions:

diophantus-13
    ………………………………………………………………………………………

and

diophantus-14
    ………………………………………………………………………………………

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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