# Easy Number Theory

You are told that positive integers $$a, b$$ exist such that $$a | b^2 , a^6 | b^7 , a^{11} | b^{12} , \ldots$$ and $$b^4 | a^5 , b^9 | a^{10} , b^{14} | a^{15} ...$$

You are also told that $$a = 20$$.

Find the number of possible values $$b$$ that exist.

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