Question

prove that if gcd(a,b)=1 then gcd (a-b,a+b,ab)=1

Answer #1

Given that the gcd(a, m) =1 and gcd(b, m) = 1. Prove that gcd(ab,
m) =1

4. Let a, b, c be integers.
(a) Prove if gcd(ab, c) = 1, then gcd(a, c) = 1 and gcd(b, c) =
1. (Hint: use the GCD characterization theorem.)
(b) Prove if gcd(a, c) = 1 and gcd(b, c) = 1, then gcd(ab, c) =
1. (Hint: you can use the GCD characterization theorem again but
you may need to multiply equations.)
(c) You have now proved that “gcd(a, c) = 1 and gcd(b, c) = 1 if
and...

Prove that if a|n and b|n and gcd(a,b) = 1 then ab|n.

Prove that if gcd(a,b)=1 and c|(a+b), then
gcd(a,c)=gcd(b,c)=1.

Prove that if a > b then gcd(a, b) = gcd(b, a mod b).

Prove that for all non-zero integers a and b, gcd(a, b) = 1 if
and only if gcd(a, b^2 ) = 1

How can I prove that if a>b>0, gcd(a,b) =
gcd(a-b,b)

suppose p is a prime number and p2 divides ab and gcd(a,b)=1.
Show p2 divides a or p2 divides b.

Suppose a,b,c belong to Z and gcd(b,c) = 1 . Prove that if
b/(ac), then b/a.

1. (a) Let a, b and c be positive integers. Prove that gcd(ac,
bc) = c x gcd(a, b). (Note that c gcd(a, b) means c times the
greatest common division of a and b)
(b) What is the greatest common divisor of a − 1 and a + 1?
(There are two different cases you need to consider.)

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