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Is it possible for a hash function, SHA256 for example, to be a cyclic hash function, where the hash of the hash returns the original value?

Example:

SHA256(a) = b
SHA256(b) = a

Or in another form:

SHA256(SHA256(a)) = a

A math example would be

f(x) = 1/x

because f(5) = 1/5, and f(1/5) return the original 5. f(f(5)) = 5.

Evan Su
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