�ber die Anzahl der Teiler einer nat�rlichen Zahl, welche die Formp?1 haben

A cyclotomic generalization of the sequence \gcd (a^n-1,b^n-1)

“…The result in [1] from which this is derived is an improvement of a result of Prachar [13]: Theorem 1.3. [13] Let δ(n) denote the number of divisors of n of the form p − 1, with p prime.…”

“…It is interesting to note that in [13], Prachar was motivated by a paper of Nöbauer [12] which dealt with the group of invertible polynomial functions on Z/nZ and particularly the subgroup of functions of the form x k , whereas in [1], Adleman, Pomerance and Rumely were motivated by the computation of a lower bound on the running time of a primality testing algorithm.…”

“…[13] Let δ(n) denote the number of divisors of n of the form p − 1, with p prime. Then there exist infinitely many n such that δ(n) > exp(c log n/(log log n) 2 ).…”

On the Greatest Prime Factor of Some Divisibility Sequences

“…The first author would like to thank Ram Murty for reference [10] and the comment regarding the size of ω(a n − 1), Jeff Bleaney for Example 1.8, and Adam Felix for comments on earlier versions of this paper.…”

Primality Testing and Jacobi Sums

“…This is a sharpening of a result of Prachar [20] that is due to Pomerance and Odlyzko. For the proof we refer to [1, Section 6].…”