【摘要】 以g（a₁,a₂,…,a_n）表n元整系数线性型a₁x₁+…+a_nx_n,a_i>0,（a₁,…,a_n）=1,不可非负整表出之最大整数,D_n-1=(a₁,…,a_n-1).注记中将证明g（a₁,…,a_n）=D_n-1·g(a₁/D_n-1,…,a_n-1/D_n-1,a_n)+(D_n-1-1)a_n。并由此对Brayer关于g（a₁,…,a_n）之上确界的著名结果和Roberts关于g（a,a+d,…,a+sd）的精确结果分别给出一个十分简洁的新证明.更多还原

【Abstract】 Let g (a1…,an) be the greatest integer N for which the Diophantine equation a1xi=N has no solution in non-negative integers, where (a1,…,an)=1.In this note, the following result is proved: g(a1,…,an)=Dn-1(Dn-1-1)an,where Dn-1=gcd (a1,…,an-1).From this, we provide a very simple proof for the Brauer’s result and Roberts’s result respectively.更多还原