GCD of Multiples equals Multiple of GCD?

Number Theory Level 3

True or False?

For any triplets of non-zero integers $(a,b,c)$ , $\gcd(ca,cb)=c \times \gcd(a,b)$ is fulfilled.

True False

1 solution

Muhammad Rasel Parvej
Dec 12, 2016

As the $gcd$ is defined to be positive, the right side always must remain positive. But for $c<0$ , the left side become negative, breaking the equality.

But, $\gcd(ca,cb)=\mid c \mid \times \gcd(a,b)$ always holds.

GCD of Multiples equals Multiple of GCD?

1 solution

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