4. (a) Let Q = {: a, b € Z, b+ 0, ged(a, b) = 1} be the set of rational numbers. An integer p is called a prime number if p has only two factors; 1 and p itself. Prove that p is not a rational number. Hence or otherwise verify the irrationality of /3.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 13E: 13. Prove that if and are rational numbers such that then there exists a rational number such...
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4. (a) Let Q = {: a, b e Z, b+ 0, ged(a, b)
An integer p is called a prime number if p has only two factors; 1 and p itself.
Prove that p is not a rational number. Hence or otherwise verify the
irrationality of 3.
=1} be the set of rational numbers.
Transcribed Image Text:4. (a) Let Q = {: a, b e Z, b+ 0, ged(a, b) An integer p is called a prime number if p has only two factors; 1 and p itself. Prove that p is not a rational number. Hence or otherwise verify the irrationality of 3. =1} be the set of rational numbers.
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