History of Hindu Mathematics: A Source Book v2.c17.s15.35

v2.c17.s15.35

He has not adduced proofs. We presume that he knew a proof at least of the first proposition. For he must have recognised the simple relation $b₁ = a₁n - k₁a,$ which has been expressly stated by Nârâyaṇa (1350). This shows at once that b₁ will be a whole number, if k₁ is so. This is also evident from the equation, Na₁² + k₁ = b₁², itself. Hence, it now remains to prove that k₁ is an integral number.