## 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

Amer Array Axiom Clearly coefficient complex number condition congruent corresponding to p"qfi cyclotomic equation corresponding cyclotomic matrix cyclotomic numbers define the cyclotomic difference set modulo eth powers eth-power character exactly exponent finite difference sets finite fields fixed fN fN following lemma forms a difference fourth power Further Galois domains GF(p GF(q group isomorphic Hence implies integers Jacobi sum Jx(m Lehmer Lemma 13 Lemma 20 Lemma 3(d Math natural numbers number of solutions numbers are given odd prime ordered pairs p'qfi 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 relations remark representation of q representation q representations of p"qfi result root of unity set in G square in G Theorem 15 theory of cyclotomy uniquely determined Whiteman y e G y'eG yields