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Finite Difference Sets
CYCLOTOMY AND DIFFERENCE SETS
The case e 2
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Array Axiom Clearly coefficient complex number cyclotomic classes cyclotomic equation corresponding cyclotomic matrix cyclotomic numbers define the cyclotomic determine the cyclotomic difference set modulo eth powers eth-power character exponent finite difference sets finite fields following lemma forms a difference fourth power Further Galois domains GD(pV GF(p GF(q group isomorphic Hence ifff implies integers isomorphic Jacobi sum Jx(m Lemma 13 Lemma 20 Lemma 3(d mod q natural numbers number of solutions numbers are given odd prime ordered pairs parameters Pell equation perfect planar difference planar difference sets power in G prime power primitive root proof of Lemma quadratic quadratic equations quadratic residues regular polygon remark representation of p"qp representation of q representation q result ri ri ri root of unity set C0 set in G Similarly square in G Theorem 15 theory of cyclotomy THOMAS STORER uniquely determined y'eG yields