Is it possible to find such integer pair $(a,n)$ that :
$\begin{cases} 5^a+1 \equiv 0 \pmod {3\cdot 2^n-1} \\ 3\cdot 2^{n-1}-1 \equiv 0 \pmod a\\ \end{cases}$
where $n \equiv 3 \pmod 4$
Is it possible to find such integer pair $(a,n)$ that :
$\begin{cases} 5^a+1 \equiv 0 \pmod {3\cdot 2^n-1} \\ 3\cdot 2^{n-1}-1 \equiv 0 \pmod a\\ \end{cases}$
where $n \equiv 3 \pmod 4$