Power e in RSA-encryption algorithm

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I'm busy with the RSA-encryption algorithm. I figured out why $0≤C≤25$ and $ ∈ {2,3,...,m−2}$ But I can't find why $ ∈ {2, 3, ... , ( − 2)}$ in the RSA-encryption algorithm with $C≡P^e(modn)$?

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This is not needed, it is just common sense. Why would make $e$ larger than necessary? Even your range can made smaller if you use the Carmichael function $\lambda(n),$ see Wikipedia or RFC 8017.

What you really need is $\gcd(\varphi(n),e)=1$ in order to compute the decryption exponent with $e d \equiv 1 \bmod{\varphi(n)}$