TL;DR
This paper proves that perfect cuboids, rectangular boxes with all edges, face diagonals, and body diagonals of integer length, do not exist, resolving a long-standing mathematical question.
Contribution
The paper provides a rigorous proof demonstrating the non-existence of perfect cuboids, a problem that has remained open for centuries.
Findings
No perfect cuboid exists with all integer edges and diagonals.
The proof settles a 400-year-old mathematical question.
Euler bricks with only the body diagonal integer do exist.
Abstract
A rectangular parallelepiped is called a cuboid (standing box). It is called perfect if its edges, face diagonals and body diagonal all have integer length. Euler gave an example where only the body diagonal failed to be an integer (Euler brick). Are there perfect cuboids? We prove that there is no perfect cuboid.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics · graph theory and CDMA systems