O'Halloran numbers: Difference between revisions
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The surface area of a cuboid
Different cuboid configurations (may) yield different surface areas, but the surface area is always an integer and is always even.
A cuboid with l = 2,
▲ 2 × ( 1 × 1 + 1 × 1 + 1 × 1 ) = 6
2 × ( 2 × 1 + 1 × 1 + 1 × 2 ) = 10
There is no configuration which will yield a surface area of 8.
There are 16 known even integer values below 1000 which can not be a surface area for any integer cuboid. It is conjectured, though not rigorously proved, that no others exist.
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