论文标题
关于Frobenius问题，限制了系数的常见分隔线
On Frobenius problem with restrictions on common divisors of coefficients
论文作者
论文摘要
令$ m，s，t $是带有$ t \ leq s-2 $和$ a_1，a_2，\ ldots，a_s $的正整数，是$（a_1，a_2，\ ldots，a_ {s-1}）= 1 $。在本文中，我们证明，每个足够大的积极整数都可以以$a_1μ1+a_1μ1+a_2μ__2+\ ldots+a_sμ_m$ $ $ $ $a_1μ__1+a_2μ______________________M$ $ $μ_1，μ_2，\ ldots，μ_s$没有$ 1 $ 1 $ 1 $ 1 $ 1 $ 1 $ 1 $μ_1，μ_2，\ ldots，μ_n$具有$ m $ m $ th的正整数的电源大于$ 1 $。 Moreover, we show that every sufficiently large positive integer can be written as a sum of positive integers $μ_1,μ_2,\ldots,μ_n$ with no common divisor being $m$-th power of a positive integer greater than $1$ but each $s-1$ of the values of $μ_1,μ_2,\ldots,μ_s$ have a common divisor being $m$-th power of正整数大于$ 1 $。
Let $m,s,t$ are positive integers with $t\leq s-2$ and $a_1,a_2,\ldots,a_s$ are positive integers such that $(a_1,a_2,\ldots,a_{s-1})=1$. In the paper we prove that every sufficiently large positive integer can be written in the form $a_1μ_1+a_2μ_2+\ldots+a_sμ_m$, where positive integers $μ_1,μ_2,\ldots,μ_s$ have no common divisor being $m$-th power of a positive integer greater than $1$ but each $t$ of the values of $μ_1,μ_2,\ldots,μ_n$ have a common divisor being $m$-th power of a positive integer greater than $1$. Moreover, we show that every sufficiently large positive integer can be written as a sum of positive integers $μ_1,μ_2,\ldots,μ_n$ with no common divisor being $m$-th power of a positive integer greater than $1$ but each $s-1$ of the values of $μ_1,μ_2,\ldots,μ_s$ have a common divisor being $m$-th power of a positive integer greater than $1$.
