波兰科学研究院数学研究所
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作者:Michael Filaseta , Richard Moy
来源:[J].Colloquium Mathematicum(IF 0.403), 2018, Vol.154, pp.295-308IMPAS
摘要:For positive integers $n$, the truncated binomial expansions of $(1+x)^n$ which consist of all the terms of degree $\le r$ where $1 \le r \le n-2$ appear always to be irreducible. For fixed $r$ and $n$ sufficiently large, this is known to be the case. We show here that for a fixe...
作者:Michael Filaseta , Wilson Harvey
来源:[J].Acta Arithmetica(IF 0.472), 2018, Vol.182, pp.43-72IMPAS
摘要:A number of results are established showing that certain subsets of the integers can be covered by congruences with distinct moduli satisfying various restrictions. For example, the primes, the powers of $2$, the Fibonacci numbers, and the sums of two squares can each be covered ...
作者:Michael Filaseta , Brady Rocks
来源:[J].Colloquium Mathematicum(IF 0.403), 2016, Vol.145, pp.307-314IMPAS
摘要:Asymptotically, more than $2/3$ of the polynomials from a sequence of polynomials in $\mathbb Z[x]$, arising from an example associated with the Strong Factorial Conjecture, are shown to be irreducible in $\mathbb Z[x]$.
作者:Morgan Cole , Scott Dunn , Michael Filaseta
来源:[J].Acta Arithmetica(IF 0.472), 2016, Vol.175, pp.137-181IMPAS
摘要:Let $f(x)$ be a polynomial with non-negative integer coefficients. This paper produces sharp bounds $M_{1}(b)$ depending on an integer $b \in [3,20]$ such that if each coefficient of $f(x)$ is $\le M_{1}(b)$ and $f(b)$ is prime, then $f(x)$ is irreducible. A number of other relat...
作者:Michael Filaseta
来源:[J].Acta Arithmetica(IF 0.472), 1992, Vol.60, pp.213-231IMPAS
作者:Michael Filaseta , Manton Matthews, Jr.
来源:[J].Colloquium Mathematicum(IF 0.403), 2004, Vol.99, pp.1-5IMPAS
摘要:If $f(x)$ and $g(x)$ are relatively prime polynomials in $\mathbb Z[x]$satisfyingcertain conditions arising from a theorem of Capelli and if $n$ is aninteger $> N$for some sufficiently large $N$, then the non-reciprocal part of $f(x)x^{n} + g(x)$is either identically $\pm1$ or is...

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