Gather equations inside an array

I want to have the solutions to some exercises in a table. I have succeeded in doing it just by using two arrays (and breaking up the equations) with the following code:

\documentclass{article}
\usepackage{amssymb,amsmath}

\begin{document}
\noindent \textbf{1.3 (4)}
$$\begin{array}{cccccc} \textbf{(a)} & 13\equiv b \pmod{8} & \textbf{(b)} & 52\equiv b\pmod{9} & \textbf{(c)} & -8\equiv b\pmod{10}\\ & 13=8\cdot 1 +5 & & 52=9\cdot 5 +7 & & -8=10\cdot (-1) +2\\ & \therefore 13\bmod 8= 5 & & \therefore 52\bmod 9= 7 & & \therefore -8\bmod 10= 2 \\ & \therefore \text{ s{\"a}tt } b=5 & & \therefore \text{ s{\"a}tt } b=7 & & \therefore \text{ s{\"a}tt } b=7\\ \end{array}$$
$$\begin{array}{ccccccc} \textbf{(d)} & 14\equiv b\pmod{14} & \textbf{(e)} & 8\equiv b\pmod{12} & \textbf{(f)} & -23\equiv b\pmod{11}\\ & 14=14\cdot 1 +0 & & 8=12\cdot 0 +8 & & -23=11\cdot (-3) +10\\ & \therefore 14\bmod 14= 0 & & \therefore 8\bmod 12= 8 & & \therefore -23\bmod 11= 10\\ &\therefore \text{ s{\"a}tt } b=0 & & \therefore \text{ s{\"a}tt } b=8 & & \therefore \text{ s{\"a}tt } b=10\\ \end{array}$$
\end{document}


But I would like to know if it is possible to do it by embedding gathered equations into one array (as this makes more sense for me so I can keep the equations together instead of splitting them up). I tried the following code but can't get it to work:

\documentclass{article}
\usepackage{amssymb,amsmath}

\begin{document}
\noindent \textbf{1.3 (4)(a)}
$$\begin{array}{ccc} \begin{gather*} 13\equiv b \pmod{8}\\ 13=8\cdot 1 +5\\ \therefore 13\bmod 8= 5\\ \therefore \text{ s{\"a}tt } b=5\\ \end{gather*} & \begin{gather*} 52\equiv b\pmod{9}\\ 52=9\cdot 5 +7\\ \therefore 52\bmod 9= 7\\ \therefore \text{ s{\"a}tt } b=7\\ \end{gather*} & \begin{gather*} -8\equiv b\pmod{10}\\ -8=10\cdot (-1) +2\\ \therefore -8\bmod 10= 2\\ \therefore \text{ s{\"a}tt } b=7\\ \end{gather*}\\ \begin{gather*} 14\equiv b\pmod{14}\\ 14=14\cdot 1 +0\\ \therefore 14\bmod 14= 0\\ \therefore \text{ s{\"a}tt } b=0\\ \end{gather*} & \begin{gather*} 8\equiv b\pmod{12}\\ 8=12\cdot 0 +8\\ \therefore 8\bmod 12= 8\\ \therefore \text{ s{\"a}tt } b=8\\ \end{gather*}& \begin{gather*} -23\equiv b\pmod{11}\\ -23=11\cdot (-3) +10\\ \therefore -23\bmod 11= 10\\ \therefore \text{ s{\"a}tt } b=10\\ \end{gather*} \end{array}$$
\end{document}


\documentclass{article}
$\setlength\arraycolsep{12pt} % more space between columns \begin{array}{ccc} \begin{gathered}% it is designed for use inside math environment 13\equiv b \pmod{8}\\ 13=8\cdot 1 +5\\ \therefore 13\bmod 8= 5\\ \therefore \text{ s{\"a}tt } b=5\\ \end{gathered} % <--- & \begin{gathered} % <--- 52\equiv b\pmod{9}\\ 52=9\cdot 5 +7\\ \therefore 52\bmod 9= 7\\ \therefore \text{ s{\"a}tt } b=7\\ \end{gathered} % <--- & \begin{gathered} % <--- -8\equiv b\pmod{10}\\ -8=10\cdot (-1) +2\\ \therefore -8\bmod 10= 2\\ \therefore \text{ s{\"a}tt } b=7\\ \end{gathered} % <--- \\ % second row \begin{gathered} % <--- 14\equiv b\pmod{14}\\ 14=14\cdot 1 +0\\ \therefore 14\bmod 14= 0\\ \therefore \text{ s{\"a}tt } b=0\\ \end{gathered} % <--- & \begin{gathered} % <--- 8\equiv b\pmod{12}\\ 8=12\cdot 0 +8\\ \therefore 8\bmod 12= 8\\ \therefore \text{ s{\"a}tt } b=8\\ \end{gathered} % <--- & \begin{gathered} % <--- -23\equiv b\pmod{11}\\ -23=11\cdot (-3) +10\\ \therefore -23\bmod 11= 10\\ \therefore \text{ s{\"a}tt } b=10\\ \end{gathered} % <--- \end{array}$