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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