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Several function Theorems

2025-02-28 Update From: SLTechnology News&Howtos shulou NAV: SLTechnology News&Howtos > Network Security >

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1. A deep understanding of the meaning and transformation represented by congruence and equations

A ≡ 1 mod n is equivalent to a mod n = 1

two。 The concept of inverse element

1 > if ax mod n = 1, then an and x are said to be inverse to each other for module n.

2 > if an and n are interprime, then a has an inverse ax mod n = 1 under module n.

3. Euler function

1 >

N is a positive integer, and the number of positive integers which does not exceed n and is coprime with n is called the Euler function value of n (in essence, prime minus 1).

For example: φ (3) = φ (4) = 2

2 >

If n = p * Q and p Q are primes, then: φ (n) = (pmur1) * (QMel 1)

4. Fermat Fermat theorem

● if m is a prime and an is not a multiple of m, then

● or: if m is a prime, then

*

Example:

*

5. Euler theorem

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