Euler's Theorem states that if 'a' and 'n' are coprime integers, then the number 'a' raised to the power of Euler's totient function \( \phi(n) \) is congruent to 1 modulo 'n'. This theorem is a fundamental result in number theory and modular arithmetic, linking concepts of divisibility and the structure of integers. It also plays a significant role in understanding Eulerian paths and circuits in graph theory, where it helps determine the existence of such paths based on the degrees of vertices.
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