منابع مشابه
Carmichael Numbers in Arithmetic Progressions
We prove that when (a, m) = 1 and a is a quadratic residue mod m, there are infinitely many Carmichael numbers in the arithmetic progression a mod m. Indeed the number of them up to x is at least x1/5 when x is large enough (depending on m). 2010 Mathematics subject classification: primary 11N25; secondary 11A51.
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For (b), let Θ be any subset of Γ, x in its complement, U as in (a). The neighbourhood xU of x contains at most one element of Γ. There exists a neighbourhood of x contained in xU and not containing any element of Θ. For (c), let V = U ·U, which is compact. The intersection of Γ with V is compact, and covered by disjoint neighbourhoods of each of its points. This intersection must therefore be ...
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A vector x ∈ VA is primitive if it is of the form xog where g ∈ GL(n,A) and xo ∈ VQ. That is, it is an image of a rational point of the vectorspace by an element of the adele group. For x = (x1, . . . , xn) ∈ VQ, at almost all non-archimedean primes v the xi’s are in Zv and have greatest common divisor 1 (locally). Since elements of the adele group are in Kv almost everywhere, this property is ...
متن کاملOn Carmichael numbers in arithmetic progressions
Assuming a weak version of a conjecture of Heath-Brown on the least prime in a residue class, we show that for any coprime integers a and m > 1, there are infinitely many Carmichael numbers in the arithmetic progression a mod m.
متن کاملOn Two Functions Arising in the Study of the Euler and Carmichael Quotients
We investigate two arithmetic functions naturally occurring in the study of the Euler and Carmichael quotients. The functions are related to the frequency of vanishing of the Euler and Carmichael quotients. We obtain several results concerning the relations between these functions as well as their typical and extreme values.
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ژورنال
عنوان ژورنال: Periodica Mathematica Hungarica
سال: 2015
ISSN: 0031-5303,1588-2829
DOI: 10.1007/s10998-014-0079-3