On Sunday, June 16, 2013 8:40:13 PM UTC-4, Deep wrote: > Consider the equation (1) below. > > > > z^2 - y = x^2 (1) > > > > Conditions: z, y, x are coprime integers , y is even and non-square > > > > From (1) one gets (2) where
Question: ***** ***** Can y^2 be an integer > 1?
***** ***** > > > > (z + y^1/2)*(z - y^1/2) = x^2 (2). > > > > (2) can then be decomposed as (3) and (4) > > > > z + y^1/2 = u^2 (3) z - y^1/2 = v^2 (4); x^2 = u^2v^2 (5) > > > > (3) and (4) can be consistent if u ^2 = a + b^1/2 (6) and v^2 = a - b^1/2 (7); a^2 > b. > > > > Question: Are the equations of (1) valid? If not why not? > > > > Any helpful comments will be appreciated.