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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

1 Answer

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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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