2014/044) Find all positive integers a and b such that a(a+2)(a+8)=3^b

all of a , a + 2 and a + 8 have to be power of 3( power 0 included)

a cannot be  power of 3 >= 1 or >= 3 then a+ 2 and a+ 8 are not divisible by 3

so check a =3^ 0 = 1

 that give a + 2 = 3 and a + 8 = 9 both power of 3

so we get a(a+2)(a+8)=3 3  

so a = 1 and b= 3 is the only solution