How many are correct?

Suppose n of the following statements are true:

• The system of equations x^2 - y^2 = ku^2, x^2 + y^2 = kv^2 have no integer solutions for x,y,k,u,v all being different from 0.
• The equation x^4 + 4y^4 = z^2 have no integer solution for x,y,z all of are different from 0
• There exists infinitely many pairs of integer x,y,z,t satisfying the system of equations x^2 + y^2 = z^2, y^2 + z^2 = t^2
• If x,y,z are sides of a rational triangle then there exists positive rational numbers a and b such that one of the equation is satisfied: x^2 -2xy $\frac{a^2 - b^2}{a^2 + b^2}$ +y^2 = z^2 ; 2 -2xy $\frac{2ab}{a^2 + b^2}$ +y^2 = z^2

What is the value of n?