References
T. Beth, D. Jungnickel, and H. Lenz,Design Theory, Cambridge: Cambridge University Press (1986).
N. L. Biggs, T. P. Kirkman, mathematician,Bull. London Math. Soc. 13 (1981), 97–120.
R. C. Bose, On the application of the properties of Galois fields to the construction of hyper-Graeco-Latin squares,Sankhyā 3 (1938), 323–338.
R. C. Bose and S. S. Shrikhande, On the falsity of Euler’s conjecture about the non-existence of two orthogonal latin squares of order 4t + 2,Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 734–737.
R. C. Bose, S. S. Shrikhande, and E. T. Parker, Further results on the construction of mutually orthogonal latin squares and the falsity of Euler’s conjecture,Can. J. Math. 12 (1960), 189–203.
A. E. Brouwer, Recursive constructions of mutually orthogonal latin squares, pp. 149-168 of [11].
A. E. Brouwer, C. J. Colbourn, and J. H. Dinitz, Mutually orthogonal latin squares, inCRC Handbook of Combinatorial Designs (C. J. Colbourn and J. H. Dinitz, eds.), Boca Raton, FL, CRC Press (1995).
R. H. Brack and H. J. Ryser, The non-existence of certain finite projective planes,Can. J. Math. 1 (1949), 88–93.
S. Chowla and H. J. Ryser, Combinatorial problems,Can..Math. 2 (1950), 93–99.
J. Dénes and A. D. Keedwell,Latin Squares and Their Applications, New York: Academic Press (1974).
J. Denes and A. D. Keedwell,Latin Squares, Annals of Discrete Math., Vol. 46, North-Holland, Amsterdam, 1991.
K. Devlin, Marginal interest,Focus 14 (1994), 16.
S. T. Dougherty, A coding theoretic solution to the 36 officer problem,Designs, Codes Cryptogr. 4 (1994), 123–128.
L. Euler, Recherches sur une nouvelle espèce de quarrés magiques,Verh. Zeeuwsch Genootsch. Wetensch. Vlissengen 9 (1782), 85–239.
L. Euler,Opera Omnia (Collected Works), Leipzig: Teubner (1911).
P. Höhler, Eine Verallgemeinerung von orthogonalen lateinischen Quadraten auf höhere Dimensionen, Diss. Dokt. Math. Eidgenöss Techn. Hochschule Zürich, 1970.
C. W. H. Lam, L. Thiel, and S. Swiercz, The non-existence of finite projective planes of order 10,Can. J. Math. 41 (1989), 1117–1123.
C. F. Laywine, G. L. Mullen, and G. Whittle,D-dimensional hypercubes and the Euler and MacNeish conjectures,Monatsh. Math. 119 (1995), 223–238.
J. H. van Lint and R. M. Wilson,A Course in Combinatorics, Cambridge: Cambridge University Press (1992).
H. F MacNeish, Euler squares,Ann. Math. 23 (1922), 221 - 227.
E. H. Moore, Tactical memoranda I-III,Am. J. Math. 18 (1896), 264–303.
G. L. Mullen and G. Whittle, Point sets with uniformity properties and orthogonal hypercubes,Monatsh. Math. 113 (1992), 265–273.
E. T. Parker, Construction of some sets of mutually orthogonal latin squares,Proc. Am. Math. Soc. 10 (1959), 946–949.
E. T. Parker, Orthogonal latin squares,Proc. Nat. Acad. Sci. U.S.A. 21 (1960), 859–862.
S. S. Shrikhande, A note on mutually orthogonal latin squares,Sankhyā, Series A 23 (1961), 115–116.
D. R. Stinson, A short proof of the nonexistence of a pair of orthogonal latin squares of order six,J. Combinat. Theory Series A 36 (1984), 373–376.
A. P. Street and D. J. Street,Combinatorics of Experimental Design, Oxford: Clarendon Press (1987).
R. M. Wilson, Concerning the number of mutually orthogonal latin squares,Discrete Math. 9 (1974), 181–198.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mullen, G.L. A candidate for the “next fermat problem”. The Mathematical Intelligencer 17, 18–22 (1995). https://doi.org/10.1007/BF03024365
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03024365