O'Halloran numbers: Difference between revisions

simplify preface
(it is not a conjecture)
(simplify preface)
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{{draft task}}
 
For this task, for our purposes, a regular integer cuboid is a regular 3 -dimensional rectangular object, with six faces, where all angles are right angles, where opposite faces of the cuboid are equal, and where each dimension is a positive integer unit length. It will subsequently be referred to simply as a cuboid; but be aware that it references the above definition.
 
The surface area of a cuboid so-defined is two times the length times the width, plus two times the length times the height, plus two times the width times the height. A cuboid will always have an even integer surface area. The minimum surface area a cuboid may have is 6; one where the '''l''', '''w''', and '''h''' measurements are all 1.:
 
2 × ( l × w + w × h + h × l )
2 × ( 1 × 1 + 1 × 1 + 1 × 1 ) = 6
 
DifferentNotice cuboidthat configurationsthe (may) yield differenttotal surface areas,area butof thea surface areacuboid is always an integer and is always even.
 
AFor example, a cuboid with l = 2, w = 1 h = 1 has a surface area of 10:
 
2 × ( 2 × 1 + 1 × 1 + 1 × 2 ) = 10
 
ThereNotice there is no configuration which will yield a surface area of 8.
 
In fact, there are 16 even integer values greater than 6 and less than 1000 which can not be the surface area of any integer cuboid.
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