Question
Prove: If p and q are primes and p 6= q, then (pq) = (p 1)(q 1). The procedure of proof should follow the following
Prove: If p and q are primes and p 6= q, then (pq) = (p 1)(q 1).
The procedure of proof should follow the following format. The answer should like that.
Example
Prove:For all integers a,b,c,m where m > 0, if ab (mod m) and bc (mod m),then ac (mod m)
Proof. Let a,b,c,m be arbitrary integers, suppose that m > 0.
(1)Suppose that ab (mod m) and bc (mod m)
(2)From (1) and using a result from last class, we conclude that m(a-b) and m(b-c)
(3)From (2) and the definition of divides, a-b = mk1and b-c = mk2for some integers k1and k2
(4)From (3), we write (a-b) + (b-c) = mk1+ mk2= m(k1+ k2),which means that a - c = m(k1+ k2). By definition of divides, m(a-c)
(5)From (4) and a result from last class, m(a-c) implies that ac (mod m).
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started