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 , Sergei Konyagin 来源：[J].Acta Arithmetica(IF 0.472), 1996, Vol.74, pp.191-205IMPAS
 作者：Michael Filaseta 来源：[J].Acta Arithmetica(IF 0.472), 1988, Vol.50, pp.133-145IMPAS
 作者：Michael Filaseta , Ognian Trifonov 来源：[J].Acta Arithmetica(IF 0.472), 1994, Vol.67, pp.323-333IMPAS
 作者：Michael Filaseta 来源：[J].Acta Arithmetica(IF 0.472), 1993, Vol.64, pp.249-270IMPAS
 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...