Rational number

The Pythagorean equation x^2 + y^2 = z^2 (to be solved over the positive integers N) is a much-studied one; many articles have appeared in this magazine alone, devoted to this equation. A close relative to this is the equation 1/x + 1/y = 1/z (which can be written as x^−1 + y^−1 = z^−1 ; in this form, its similarity to the Pythagorean equation is readily seen), and this too has been studied many times in At Right Angles.

In this edition of ‘Adventures’ we study a few miscellaneous problems, some from past RMOs. As usual, we pose the problems first and give the solutions later in the article, thereby giving you an opportunity to work on the problems.

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