History of Hindu Mathematics: A Source Book v2.c17.s14.145

v2.c17.s14.145

It can be proved easily that these values of x, y are integral. For, if β is even, β² + 2 is also even. Therefore, the above values of x, y are integral. If on the contrary β is odd, β² is also odd ; then β² + 1 and β² + 3 are even. Hence in this case also the above values are integral.