Answer to Question #72142 in Discrete Mathematics for Looi

Question

Prove or disprove the following statement.
“Let p and q be positive integers, if p mod 4 = 1 and q mod 4 = 2, then pq mod 4 = 2.”

Answer 1

Solution:- It is given that
p (mod 4) = 1 and q (mod 4) = 2
Let p = 4a + 1 and q = 4b + 2, for some non-negative integers a and b.

Now pq = (4a + 1)(4b + 2)
= 16ab + 4b + 8a + 2
Now, it is clear that pq (mod 4) = 2 because 4 divides 4, 8 and 16.
Hence Proved.