Show that ab and ac2 then a2bc2 where a b and c are nonzero

Show that a|b and a|(c+2), then a²|b(c+2), where a, b and c are nonzero integers.

Give an example of three integers a,b and c satisfying this property.

Solution

a|b

b=ma

a|c+2

c+2=na

b(c+2)=mn*a^2

Hence, a^2|m+n

example

a=2,b=2,c=2