Is parametrization necessary?

I want to construct a rectangle such that

  • it has integer dimensions a×ba \times b that differ by exactly 1 (i.e. ab=1);(\text{i.e. }|a-b|=1);
  • its diagonal also has an integer length.

The diagram to the right shows such a rectangle.

Is there any other way to construct a rectangle satisfying the above properties?


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