25,190 research outputs found
Divisors of the Euler and Carmichael functions
We study the distribution of divisors of Euler's totient function and
Carmichael's function. In particular, we estimate how often the values of these
functions have "dense" divisors.Comment: v.3, 11 pages. To appear in Acta Arithmetica. Very small corrections
and changes suggested by the referee. Added abstract, keywords, MS
On numbers dividing the th term of a linear recurrence
Here, we give upper and lower bounds on the count of positive integers dividing the th term of a nondegenerate linearly recurrent sequence with
simple roots
Around Pelikan's conjecture on very odd sequences
Very odd sequences were introduced in 1973 by J. Pelikan who conjectured that
there were none of length >=5. This conjecture was disproved by MacWilliams and
Odlyzko in 1977 who proved there are in fact many very odd sequences. We give
connections of these sequences with duadic codes, cyclic difference sets,
levels (Stufen) of cyclotomic fields, and derive some new asymptotic results on
their lengths and on S(n), which denotes the number of very odd sequences of
length n.Comment: 21 pages, two tables. Revised version with improved presentation and
correction of some typos and minor errors that will appear in Manuscripta
Mathematic
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