Euler's Theorem is a result in number theory that states that for any positive integers a and n that are relatively prime (i.e., their greatest common divisor is 1), the following equation holds:

a^(phi(n)) = 1 (mod n)

where phi(n) is Euler's totient function, which gives the number of positive integers less than n that are relatively prime to n.

In other words, Euler's Theorem states that if a and n are relatively prime, then a raised to the power of phi(n) is congruent to 1 modulo n. This result has important applications in cryptography, coding theory, and publickey encryption. For example, Euler's Theorem is used in RSA encryption, one of the most widely used publickey encryption algorithms.
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