Congratulations, you have reached the end of this lesson! Let’s recap what we learned:

- We say that, for integers a, b, and n with n > 0,
*a is congruent to b mod n*if n divides (a-b). Equivalently, a is congruent to b mod n if there exists some integer k for which`a-b = n*k`

is true. We write this mathematically as:

`$a \equiv b\;(mod\;n)$`

The

*reflexive property*for congruences states that a is congruent to a mod n.The

*symmetric property*for congruences states that, if a is congruent to b mod n, then b is congruent to a mod n.The

*transitive property*for congruences says that, if a is congruent to b mod n and b is congruent to c mod n, then a is congruent to c mod nWe can solve for congruences and linear congruences using a procedure that is analogous to solving for the variable

`x`

in a linear equation. The only differences are that congruences must perform modular arithmetic after each step and that the solution of a congruence problem has many possibilities for the value of the unknown variable.

### Instructions

**1.**

Suppose we have the following congruence:

`$5a \equiv 8\;(mod\;5)$`

Create a variable called `answer`

and set it to either `True`

if you think this congruence can be solved or `False`

if you think this congruence cannot be solved.