## Cyclotomy and difference sets |

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### Contents

Finite Difference Sets | 13 |

CYCLOTOMY AND DIFFERENCE SETS | 24 |

The case e 2 | 30 |

Copyright | |

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### Common terms and phrases

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