Equation 


$$(2x^2+1)(2y^2+1)=4z^2+1$$ 


has no solutions in the positive integers. Its true?



$(2x^2+1)(2y^2+1)=4z^2+1$ has no positive integer solutions?
By popular demand, I turn my comment to an answer:


There are no solutions according to Theorem 6 in Kashihara: Explicit complete solution in integers of a class of equations $(ax^2−b)(ay^2−b)=z^2−c$, Manuscripta Math. 80 (1993), 373-392.


