Hi everyone,

Problem #20 in Chapter 5 uses an idea that we have *not* yet covered in class. **Â 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. Â 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). Â The problem reliesÂ on a new definition, that of congruence mod n – itÂ appears in the book as Definition 5.1 on page 105, but I will also give it here:

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

.

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

Â (by the definition of congruence), and

for some integer (by the definition of divides)

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

Best of luck,

Prof. Reitz