Let p be prime. Prove that Z(p) ={a/b: a,b ? Z and gcd(b,p)=1}

onthewevd

onthewevd

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2022-09-01

Let p be prime. Prove that
Z(p) ={a/b: a,b ? Z and gcd(b,p)=1}

Answer & Explanation

historia075c

historia075c

Beginner2022-09-02Added 6 answers

given Z(p) = a/b; and a,b ? Z
b can be any number other than zero else Z(p) becomes infinity.
p is a prime number,
so the factors of p are: p,1
b can have any factors but the 1 is the compulsory factor
and 1 is the only common factor.
so the maximum of possible greatest common divisor for b and p is 1.

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