47 research outputs found

    Linear Complexity of A Family of Binary pq2 -periodic Sequences From Euler Quotients

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    We first introduce a family of binary pq2pq^2 -periodic sequences based on the Euler quotients modulo pqpq, where pp and qq are two distinct odd primes and pp divides qāˆ’1q - 1. The minimal polynomials and linear complexities are determined for the proposed sequences provided that 2qāˆ’1ā‰”Ģø1(modq)22^{q-1} \not \equiv 1 \pmod q^2 . The results show that the proposed sequences have high linear complexities

    Artin's primitive root conjecture -a survey -

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    This is an expanded version of a write-up of a talk given in the fall of 2000 in Oberwolfach. A large part of it is intended to be understandable by non-number theorists with a mathematical background. The talk covered some of the history, results and ideas connected with Artin's celebrated primitive root conjecture dating from 1927. In the update several new results established after 2000 are also discussed.Comment: 87 pages, 512 references, to appear in Integer
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