A perfect cuboid is a cuboid having integer side lengths, integer face diagonals d_(a b) | = | sqrt(a^2 + b^2) d_(a c) | = | sqrt(a^2 + c^2) d_(b c) | = | sqrt(b^2 + c^2), and an integer space diagonal d_(a b c) = sqrt(a^2 + b^2 + c^2). The problem of finding such a cuboid is also called the brick problem, diagonals problem, perfect box problem, perfect cuboid problem, or rational cuboid problem.
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