MathDB

Let

k

be a fixed positive integer. For each integer

1 \leq i \leq 4

, let

x_i

and

y_i

be positive integers such that their least common multiple is

k

. Suppose that the four points

(x_1, y_1)

(x_2, y_2)

(x_3, y_3)

(x_4, y_4)

are the vertices of a non-degenerate rectangle in the Cartesian plane. Prove that

x_1x_2x_3x_4

is a perfect square.
Andrei Chirita

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