Question

What is the purpose of Euler's theorem?

Answer 1

Explanation:

Euler's theorem shows why raising a to the power φ(m) + 1 in base m keeps the last digit the same, but only if a is relatively prime to m. To extend the fifth root trick to other bases you'll have a little more work to do.

Why do we use Euler's theorem?

Euler's theorem underlies RSA cryptosystem, which is widely used in Internet communications. In this cryptosystem, Euler's theorem is used with n being a product of two large prime numbers, and the security of the system is based on the difficulty of factoring such an integer.

Answer 2

Answer:

Euler's theorem shows why raising a to the power φ(m) + 1 in base m keeps the last digit the same, but only if a is relatively prime to m. To extend the fifth root trick to other bases you'll have a little more work to do.

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