Bruck-Ryser-Chowla Theorem

If , and the Squarefree part of is divisible by a Prime , then noDifference Set of Order exists. Equivalently, if aProjective Plane of order exists, and or 2 (mod 4), then is the sum of twoSquares.

Dinitz and Stinson (1992) give the theorem in the following form. If a symmetric -Block Designexists, then

1. If is Even, then is a Square Number,

2. If is Odd, then the Diophantine Equation

has a solution in integers, not all of which are 0.

References

Dinitz, J. H. and Stinson, D. R. ``A Brief Introduction to Design Theory.'' Ch. 1 in Contemporary Design Theory: A Collection of Surveys (Ed. J. H. Dinitz and D. R. Stinson). New York: Wiley, pp. 1-12, 1992.

Gordon, D. M. ``The Prime Power Conjecture is True for .'' Electronic J. Combinatorics 1, R6 1-7, 1994.http://www.combinatorics.org/Volume_1/volume1.html#R6.

Ryser, H. J. Combinatorial Mathematics. Buffalo, NY: Math. Assoc. Amer., 1963.

• Mertens Conjecture
• Mertens Constant
• Mertens Function
• Mertens Theorem
• Mertz Apodization Function
• Mesh Size
• Mesokurtic
• M-Estimate
• Metabiaugmented Dodecahedron
• Metabiaugmented Hexagonal Prism
• Metabiaugmented Truncated Dodecahedron
• Metabidiminished Icosahedron
• Metabidiminished Rhombicosidodecahedron
• Metabigyrate Rhombicosidodecahedron
• Metadrome
• Metagyrate Diminished Rhombicosidodecahedron
• Metalogic
• Metamathematics
• Method
• Metric
• Metric Entropy
• Metric Equivalence Problem
• Metric Space
• Metric Tensor
• Mex