# Recognizing the Square Numbers!

$(2^n -1), \ \ (3^{2n}-1), \ \ (4^{3n}-1), \ \ (5^{4n}-1),\ \ (6^{5n}-1), \ \ (7^{6n}-1),\ \ (8^{7n}-1),\ \ (9^{8n}-1)$

In Calvin's number set, there are the numbers as listed above for each natural number $$n$$, and there are no other numbers in the set. How many square numbers does this set contain?

Note : The set of Natural Numbers doesn't contain the number $$0$$.

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