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Problems > The Maine Page > 2002

Complex Proof

Let x and y be real integers such that x > y > 0. If a + bi is the square of x + yi, prove that a and b are the legs in a pythagorean triple -- that is, if a and b are whole number lengths of the legs in a right triangle, the hypotenuse will also be a whole number. (i is the imaginary unit.)

For 2 bonus points, specify less restrictive conditions on the integers x and y for which the above statement is still true.


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Thanks, Soroban

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