Primitive root bias for twin primes II: Schinzel-type theorems for totient quotients and the sum-of-divisors function
نویسندگان
چکیده
منابع مشابه
On the Ratio of the Sum of Divisors and Euler’s Totient Function I
We prove that the only solutions to the equation σ(n) = 2 · φ(n) with at most three distinct prime factors are 3, 35 and 1045. Moreover there exist at most a finite number of solutions to σ(n) = 2 ·φ(n) with Ω(n) ≤ k, and there are at most 22 k+k − k squarefree solutions to φ(n) ∣∣σ(n) if ω(n) = k. Lastly the number of solutions to φ(n) ∣∣σ(n) as x→∞ is of order O (x exp (−1 2log x)).
متن کاملthe search for the self in becketts theatre: waiting for godot and endgame
this thesis is based upon the works of samuel beckett. one of the greatest writers of contemporary literature. here, i have tried to focus on one of the main themes in becketts works: the search for the real "me" or the real self, which is not only a problem to be solved for beckett man but also for each of us. i have tried to show becketts techniques in approaching this unattainable goal, base...
15 صفحه اولthe investigation of the relationship between type a and type b personalities and quality of translation
چکیده ندارد.
Bounded gaps between primes with a given primitive root, II
Let m be a natural number, and let Q be a set containing at least exp(Cm) primes. We show that one can find infinitely many strings of m consecutive primes each of which has some q ∈ Q as a primitive root, all lying in an interval of length OQ(exp(C ′m)). This is a bounded gaps variant of a theorem of Gupta and Ram Murty. We also prove a result on an elliptic analogue of Artin’s conjecture. Let...
متن کاملOn Square Values of the Product of the Euler Totient and Sum of Divisors Functions
If n is a positive integer such that φ(n)σ(n) = m for some positive integer m, then m 6 n. We put m = n − a and we study the positive integers a arising in this way.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2020
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2019.08.003