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Computing Multiplicative Order and Primitive Root in Finite Cyclic Group
Multiplicative order of an element of group is the least positive
integer such that , where is the identity element of . If the
order of an element is equal to , it is called generator or primitive
root. This paper describes the algorithms for computing multiplicative order
and primitive root in , we also present a logarithmic
improvement over classical algorithms.Comment: 8 page
Primitive divisors of Lucas and Lehmer sequences
Stewart reduced the problem of determining all Lucas and Lehmer sequences
whose -th element does not have a primitive divisor to solving certain Thue
equations. Using the method of Tzanakis and de Weger for solving Thue
equations, we determine such sequences for . Further computations
lead us to conjecture that, for , the -th element of such sequences
always has a primitive divisor
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