设同时满足条件：\(①b_{n}+b_{n+2}\geqslant 2b_{n+1}\)；\(②b_{n}\leqslant M(n∈N^{*},M\)是常数\()\)的无穷数列\(\{b_{n}\}\)叫“欧拉”数列\(.\)已知数列\(\{a_{n}\}\)的前\(n\)项和\(S_{n}\)满足\((a-1)S_{n}=a(a_{n}-1)(a\)为常数，且\(a\neq 0\)，\(a\neq 1)\)．
\((1)\)求数列\(\{a_{n}\}\)的通项公式；
\((2)\)设\(b_{n}= \dfrac {S_{n}}{a_{n}}+1\)，若数列\(\{b_{n}\}\)为等比数列，求\(a\)的值，并证明数列\(\{ \dfrac {1}{b_{n}}\}\)为“欧拉”数列．