Please show the work for the following questions:

1. Find a solution to the Diophantine equation 2x^2+5xy+y^2=13, or prove that there is no solution
2. Let be a positive square number. Recall that h() is the nuber of classes of primitive binary quadratic forms of discriminant . Demonstrate that every such form has a double-lake or else has a unique rivermouth: a triad around which the values are negative positive-zero in clockwise orientation. Use this to derive an exact formula for h()
3. Demonstrate that there cannot be a set of four lax vectors, any two of which form a basis