Hi everyone,

Problem #20 in Chapter 5 uses an idea that we have *not* yet covered in class. **Ā It is no longer a required problem – you don’t have to do it** – but I will give you extra credit if you turn in a solution. Ā This is *excellent practice* in reading and applying a definition (just as we have been doing for the definitions of odd, even, divides, and so on). Ā The problem reliesĀ on a new definition, that of congruence mod n – itĀ appears in the book as Definition 5.1 on page 105, but I will also give it here:

**Definition**. Ā Given integers *a* and *b*, and , we say “a is congruent to b mod n”, orĀ , if

.

For example, if are told that , then we can conclude:

Ā (by the definition of congruence), and

for some integer (by the definition of divides)

Hope this helps! Ā Please write back and let me know if you have any questions.

Best of luck,

Prof. Reitz