The coprime-coefficients conjecture for restricted Frobenius representations

Let $s\ge 3$. Let $a_k$, where $k\in [s]$, be positive integers such that $(a_1,a_2,\ldots,a_s)=1$. Then $S_{s,s-2}^m(a_1,a_2,\ldots,a_s)$ denotes the set of positive integers satisfying the paper's restricted Frobenius representation conditions. Coprime-coefficients conjecture. There exists a computable constant $c=c(a_1,a_2,\ldots,a_s)$ such that every positive integer at least equal to $c$ belongs to the set $S_{s,s-2}^m(a_1,a_2,\ldots,a_s)$. The conjecture asks whether the paper's result remains valid when the assumption $(a_1,a_2,\ldots,a_{s-1})=1$ is weakened to $(a_1,a_2,\ldots,a_s)=1$; the source presents this as an open problem and offers no resolution.