3 papers
math.NT2026
Exponent-one blockers and a Mordell-Weil construction of Euler bricks
René Peschmann
A body cuboid is a rectangular parallelepiped with integer edges and integer face diagonals; if its space diagonal is also integer, it is a perfect cuboid, whose existence is a lon…
math.NT2026
A torsion-intersection proof of perfect-cuboid nonexistence on 1,072 explicit master-tuple fibers
René Peschmann
Building on the genus-3 reduction established in our companion paper (arXiv:2604.09328), we give an unconditional proof of the perfect-cuboid conjec…
math.NT2026
Quartic reductions and elliptic obstructions for perfect Euler bricks
René Peschmann
We show that the perfect Euler brick (perfect cuboid) problem is equivalent to the following elementary question: do there exist coprime integers such that the two exp…