History of Hindu Mathematics: A Source Book v2.c17.s14.94

v2.c17.s14.94

If m be an optional number, it is stated that 2m/(m² ~ N) is a lesser root of Nx² + 1 = y². Then, substituting that value of x in the equation, we get $y² = N(2m/(m² ~ N))² + 1,$ $= ((m² + N)/(m² ~ N))².$