Suppose ab c Z If a does not divide bc then a does not divid

Suppose a,b, c Z. If a does not divide bc, then a does not divide b.

Solution

By proving the above theory we should take the contradiction of the given part.

In the theorem says a does not divide b.

So if we take a counter part of this then a divides b.

If a divides b then b=ak for some integer k.

if we multiply both sides with c

then b = ak

and bc = akc

and c also belongs to Z and K is also belongs to Z

so the product of c and k can be taken as K\' for K\' belongs to Z.

so bc = aK\'.

that means a divides bc.So this is the contradiction of the above theorem.\\\\

so if a does not divide bc,then a does not divide b.