Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

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

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

MySQL/PHP Database Applications

Authors: Jay Greenspan, Brad Bulger

1st Edition

978-0764535376

More Books

Students also viewed these Databases questions

Question

understand the meaning of the terms discipline and grievance

Answered: 1 week ago