History of Hindu Mathematics: A Source Book v2.c17.s17.t4.21

v2.c17.s17.t4.21

If b=αβ, taking m=2β p², we easily arrive at \begin{align*} x &= \alpha q²-\beta p², \\ y &= 2pq, \\ z &= \alpha q²+\beta p², \end{align*} where p, q are arbitrary integers, as the solution in positive integers of z²=x²+by². This solution was given by A. Desboves (1879).¹