How to make the congruent symbol in Latex ?

How to make the congruent code in Latex ?

Command \cong

The command \cong is used in LaTeX to produce the “congruent” symbol. This symbol is commonly used in mathematics to indicate that two objects are congruent, i.e., they have the same dimensions and shape.

Examples of using \cong

Two triangles are congruent if they have the same three sides respectively equal:

\triangle ABC \cong \triangle DEF
\[\triangle ABC \cong \triangle DEF\]

Two angles are congruent if they have the same measure:

\angle ABC \cong \angle DEF
\[\angle ABC \cong \angle DEF\]

In arithmetic, the congruence notation is often used to indicate that two numbers are equivalent modulo a certain integer.

For example, we can write that:

6 \cong 2 \pmod{2}
\[6 \cong 2 \pmod{2}\]

This means that the difference between 6 and 2 is divisible by 2, i.e., $(6-2)$ is divisible by 2.

Example of congruence for the little theorem of Fermat

The little theorem of Fermat is an important result in number theory that uses congruences. It states that if p is a prime number and a is an integer that is not divisible by p, then:

a^{p-1} \cong 1 \pmod{p}
\[a^{p-1} \cong 1 \pmod{p}\]

This result has many applications in cryptography and number theory.