Suppose that Q(X,Y)=X2 + DY 2 properly represents 2m+2 (i.e. with relatively prime coordinates x and

Suppose that Q(X,Y)=X2 + DY 2 properly represents 2m+2 (i.e. with relatively prime coordinates x and y). Find an equivalent quadratic form Q(X,Y)=2m+2X2 +2BXY + CY2 (which trivially represents 2m+2). [ Hint Write 2m+2 = x2 + Dy2,(x,y) ? Z2 – where x and y are coprime. So, rx + sy = 1 for appropriate r,s ? Z. Then compute xy -sr 10 0 Dx -s yr . ]