Problem dossier · Number Theory
Perfect cuboid
a.k.a. Euler brick with integer space diagonal
Does a rectangular box exist whose three edges, three face diagonals, and space diagonal are all integers? Euler bricks (integer edges and face diagonals) exist; adding the space diagonal is the open part.
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Status
Open. No perfect cuboid with odd edge below ~10^13-scale search bounds; many modular obstructions known.
Think you can crack this one? Read the playbook before you announce →
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The Angle of Attack
Bounded Diophantine search over parametrizations of Euler bricks; derive and stack congruence constraints to prune; explore near-misses (six of seven integers).
Tags: diophantine · euler brick · pythagorean · search
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The Lab
No instruments built yet. When this problem gets tackled, its interactive instruments — explorers, searches, verifiers running in the browser — live here. See the Collatz dossier for what a fully tackled problem looks like.
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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Related Problems
More open problems in Number Theory and adjacent territory.
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