Published in
Cambridge University Press, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 3-4(99), p. 277-281
DOI: 10.1017/s0308210500014293
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Certain 3-decompositions of complete graphs, with an application to finite fields
Journal article published in 1985 by
Peter Rowlinson
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Abstract
SynopsisA necessary condition is obtained for a complete graph to have a decomposition as the line-disjoint union of three isomorphic strongly regular subgraphs. The condition is used to determine the number of non-trivial solutions of the equation x3+y3 = z3 in a finite field of characteristic p ≡ 2 mod 3.