A candidate for the ``Next Fermat Problem''
type: Item
instance of: scholarly article
title: A candidate for the ``Next Fermat Problem''
zbMATH Open document ID: 0845.05020
DOI: 10.1007/BF03024365
published in: The Mathematical Intelligencer
publication date: 1996-03-05T00:00:00Z
review text: Firmly rooted in Euler's work is the author's proposal for the ``Next Fermat Problem'': There exist \(n - 1\) mutually orthogonal Latin squares of order \(n\) if and only if \(n\) is a power of a prime. A case is made as to why this should become the Next Problem, and a historical sketch of this and other related conjectures and problems is provided. Generalizations to orthogonal hypercubes are also discussed.
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 851686
zbMATH Keywords: orthogonal Latin squares
zbMATH Keywords: orthogonal hypercubes
author: Gary L. Mullen
reviewed by: Chester J. Salwach
MaRDI profile type: Publication
cites work: Q3737429
cites work: T. P. Kirkman, Mathematician
cites work: ON THE FALSITY OF EULER'S CONJECTURE ABOUT THE NON-EXISTENCE OF TWO ORTHOGONAL LATIN SQUARES OF ORDER 4t + 2
cites work: Further Results on the Construction of Mutually Orthogonal Latin Squares and the Falsity of Euler's Conjecture
cites work: Q3972903
cites work: Q4876928
cites work: The Nonexistence of Certain Finite Projective Planes
cites work: Combinatorial Problems
cites work: Q4769064
cites work: Latin squares. New developments in the theory and applications
cites work: A coding theoretic solution to the 36 officer problem
cites work: Q5616181
cites work: The Non-Existence of Finite Projective Planes of Order 10
cites work: \(d\)-dimensional hypercubes and the Euler and MacNeish conjectures
cites work: Q4002255
cites work: Point sets with uniformity properties and orthogonal hypercubes
cites work: Construction of Some Sets of Mutually Orthogonal Latin Squares
cites work: ORTHOGONAL LATIN SQUARES
cites work: Q3280507
cites work: A short proof of the nonexistence of a pair of orthogonal Latin squares of order six
cites work: Q3758829
cites work: Concerning the number of mutually orthogonal latin squares
full work available at URL: https://doi.org/10.1007/bf03024365
OpenAlex ID: W2167584992
description: scientific article; zbMATH DE number 851686