History of Hindu Mathematics: A Source Book v2.c17.s25.48

v2.c17.s25.48

It should also be noted that in order that xy + β or p²q² - α(p² + q²) + α² + β may be a square, there may be other values of q besides the one specified above, namely q = p ± √(β/α). We may, indeed, regard $p²q² - α(p² + q²) + α² + β = ξ²$ as an indeterminate equation in q. Since we know one solution of it, namely q = p ± γ, ξ = p(p ± γ) - α, we can find an infinite number of other solutions by the method of the Square-nature.