T. Hakobyan

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20142018

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math.LO2016

An Ax-Kochen-Ershov Theorem for Monotone Differential-Henselian Fields

Tigran Hakobyan

Scanlon [5] proves Ax-Kochen-Ershov type results for differential-henselian monotone valued differential fields with many constants. We show how to get rid of the condition "with m…

math.NT2016

On the $P_{1}$ property of sequences of positive integers

Tigran Hakobyan

It is well-known that for any non-constant polynomial $P$ with integer coefficients the sequence $(P (n))_{n \in N}$ has the property that there are infinitely many prime nu…

math.NT2016

On the unboundedness of common divisors of distinct terms of the sequence $a_{n} = 2^{2^{n}} + d$ for $d > 1$

Tigran Hakobyan

It is well-known that for any distinct positive integers $k$ and $n$ , the numbers $2^{2^{k}} + 1$ and $2^{2^{n}} + 1$ are relatively prime. In this paper we consider the situation when 1 i…

An Ax-Kochen-Ershov Theorem for Monotone Differential-Henselian Fields

On the P1​ property of sequences of positive integers

On the unboundedness of common divisors of distinct terms of the sequence an​=22n+d for d>1

On the $P_{1}$ property of sequences of positive integers

On the unboundedness of common divisors of distinct terms of the sequence $a_{n} = 2^{2^{n}} + d$ for $d > 1$