On a Conjecture about the Number of Solutions to Linear Diophantine Equations with a Positive Integer Parameter

Sheng Chen, Nan Li

Let A(n) be a $k\times s$ matrix and $m(n)$ be a $k$ dimensional vector, where all entries of A(n) and $m(n)$ are integer-valued polynomials in $n$. Suppose that $$t(m(n)|A(n))=#\{…