My solution is as follows: Note that the digital root is simply the remainder mod 9. Let (a, a+2) be a twin prime pair where a is not 3. Then a must be 2 mod 3 so we can write a = 3m - 1 for an integer m. Then a * (a + 2) = 9m^2 - 1 which is 8 mod 9 as desired. QED Cool problem!
My solution is as follows:
Note that the digital root is simply the remainder mod 9. Let (a, a+2) be a twin prime pair where a is not 3. Then a must be 2 mod 3 so we can write a = 3m - 1 for an integer m. Then a * (a + 2) = 9m^2 - 1 which is 8 mod 9 as desired. QED
Cool problem!