# Can you tell me what power is greater?

Consider all integers $$n$$ which satisfy the following condition:

$$36! \equiv 0 \pmod{n}$$, but for all $$i < 36$$, we have $$i! \not \equiv 0 \pmod{n}$$.

The smallest positive integer value of $$n$$ that satisfies this condition can be written in the form $$a^b$$, where $$a$$ is a prime number. What is the value of $$a + b$$?

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