On Carmichael numbers in arithmetic progressions
نویسندگان
چکیده
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.
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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