Hi everyone,
Problem #20 in Chapter 5 uses an idea that we have *not* yet covered in class.  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.  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).  The problem relies on a new definition, that of congruence mod n – it 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:
 (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