论文标题
在弗罗贝尼乌斯数量上移动的功率序列
On Frobenius Numbers of Shifted Power Sequences
论文作者
论文摘要
我们解决了表征Frobenius数字$ g（a）$的开放问题，用于移动的正方形序列$ a =（a，a+1^2，\ ldots，a+k^2）$，证实了Einstein等人的猜想。 （2007）。通过将组合减少与Lagrange的四平方定理和生成功能技术相结合，我们为$ g（a）$：$ a $ a $ a $ a $ a $ a $ a $ a $ a $ k^2 $分类。
We resolve the open problem of characterizing the Frobenius number $g(A)$ for shifted square sequences $A = (a, a+1^2, \ldots, a+k^2)$, confirming a conjecture of Einstein et al. (2007). By combining a combinatorial reduction to an optimization problem with Lagrange's Four-Square Theorem and generating function techniques, we derive an explicit formula for $g(A)$: a piecewise quadratic polynomial in $a$, classified by residue classes modulo $k^2$.
