Find all primes $p$ such that $\dfrac{(2^{p-1}-1)}{p}$ is a perfect square. I tried brute-force method and tried to find some pattern. I got $p=3,7$ as solutions . Apart from these I have tried for many other primes but couldn't find any other such prime. Are these the only primes that satisfy the condition ? .
If yes , how to prove it theoretically and if not, how to find others?.
Thanks in advance!!