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**What are linear congruence equations?**

Linear congruence equations are equations of the form:

ax ≡ b (mod m)

where a, b, and m are integers, and m > 0.

The symbol ≡ means “congruent to,” and it means that the two sides of the equation have the same remainder when divided by m.

**Uses of linear congruence equations**

Linear congruence equations have many applications in mathematics, computer science, and cryptography. They are used to:

- Solve Diophantine equations.
- Generate random numbers.
- Implement encryption algorithms.

**Why study linear congruence equations?**

Studying linear congruence equations gives a strong foundation in mathematics, computer science, and cryptography. It is useful in many job roles, including that of:

**Mathematician:**Mathematicians who specialize in number theory or cryptography.**Computer scientist:**Computer scientists who work on random number generation or encryption algorithms.**Cryptographer:**Cryptographers use linear congruence equations to design and implement encryption algorithms.

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