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

 
 
1 + a \,b = A^2   …………………   1 + b \,c = D^2
1 + a \,c = B^2   …………………   1 + b \,d = E^2
1 + a \,d = C^2   …………………   1 + c \,d = F^2

 

We set   a = 2
 

a = 2
b = 2 \,(n^2 - n)
c = 2 \, n^2 + 2 \, n
d = 4 \, (8 \, n^4 - 6 \, n^2 + 1)

1 + a \,b = (2 \, n - 1)^2   ………………………   1 + b \,c = (2 \, n^2 - 1)^2
1 + a \,c = (2 \, n + 1)^2   ………………………   1 + b \,d = (8 \, n^3 - 4 \, n^2 - 4 \, n + 1)^2
1 + a \,d = (8 \, n^2 - 3)^2   …………………….   1 + c \,d = (8 \, n^3 + 4 \, n^2 - 4 \, n - 1)^2

diophantus-2

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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