2. let a, b, ce z such that ged(a, c)d for some integer d. prove that if a | bc then a | bd. [3

Answer with explanation:

It is given that, a, b and c belong to the set of integers.

→ gcd(a,c)=d

→GCD=Greatest Common Divisor

→The greatest number which divides both a and c is d.

It means d divides a, and d divides c.

 a=d k, for some integer k.(1)

  c= d m, for some integer m.(2)

Now, it is given that, a divides bc.

So,→ 'a' will divide "bdm".[using 2, as c=d m]

It shows that, a divides bd, that is a| bd.

Hence proved

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step-by-step explanation: