Re: Rational Points

Robert Israel wrote:
In article <1152236444.887809.296900@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Deep <deepkdeb@xxxxxxxxx> wrote:
The equation (1) represents an ellipse under the given conditions.

ax^2 + by^2 = r^2 (1) where r, b, a are integers > 0

Assertion: (1) cannot be satisfied for rational values of x, y.

Any comment upon the correctness of the assertion will be appreciated.

One of the most obviously false assertions you've made so far.
It's certainly false if a or b is a square. Thus if b = c^2, try
x = 2 r/(a+1), y = r (a - 1)/(c (a+1)).

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

Yes, you are right Professor Israel. Kindly note the corrections " none
of a or b is a perfect square"
Now kindly give a counter example.

.

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