Euler's Theorem states that if 'a' is an integer and 'n' is a positive integer that are coprime, then $a^{\phi(n)} \equiv 1 \pmod{n}$, where $\phi(n)$ is Euler's totient function. This theorem connects number theory and modular arithmetic, showcasing how exponentiation behaves under the modulus of integers that share no common factors.
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