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Topic: No perfect cuboids exist with smallest side < 2^32
Replies: 2   Last Post: Nov 26, 2012 3:39 AM

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Randall L. Rathbun

Posts: 62
Registered: 12/6/04
No perfect cuboids exist with smallest side < 2^32
Posted: Jul 10, 2002 10:51 PM
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Having exhaustively searched ALL integer cuboids with the smallest side
from 1 to 2^32, there are no solutions to the perfect integer cuboid in
that range.

There are subtle suggestions from the 4th pentacycle ratio of face cuboids,
that the perfect cuboid does NOT exist.

An older reference to this problem is D18 "Is there a perfect cuboid? ..."
in "Unsolved Problems in Number Theory", Richard K. Guy, 2nd edition,
Springer-Verlag, NY, ISBN 0-387-94289-0 or 3-540-94289-0, pp 173-181.

Randall






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