Correction to: The arithmetic of Carmichael quotients
نویسندگان
چکیده
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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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.
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The statements of Main Theorem 1.1 and Theorem 2.1 of the author's paper [Trans. Amer. are affected similarly.) These restrictions can be removed if the conclusions of the results are weakened to allow for the possible existence of transitive, proper subgroups of G. In this form, the results can be extended to the setting where G is a product of real and p-adic Lie groups. There are two errors ...
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ژورنال
عنوان ژورنال: Periodica Mathematica Hungarica
سال: 2017
ISSN: 0031-5303,1588-2829
DOI: 10.1007/s10998-017-0227-7