Solution of Erd\H{o}s Problem 633
Michael Beeson, Miklos Laczkovich, Yan X. Zhang
TL;DR
This paper classifies triangles that can only be tiled into a square number of congruent triangles, providing a complete solution to Erdős Problem 633.
Contribution
It offers a complete classification of such triangles, resolving Erdős Problem 633 for the first time.
Findings
Identifies all triangles that can be tiled into a square number of congruent triangles.
Proves that only specific triangle types satisfy the tiling condition.
Settles Erdős Problem 633 conclusively.
Abstract
We classify triangles that can be tiled only into a square number of congruent triangles, settling Erd\H{o}s Problem 633.
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