Let \(A={102^1, 102^2, 102^3, \cdots}\). How many primes \(p\) are there such that \(A\) has at least one element \(a\) such that \(a \equiv -1 \text{ (mod p)}\)?

For example, one such prime is \(103\), because \(102^1 \equiv -1 \text{ (mod 103)}\).

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