Hello qtpipi(a) Suppose that is represented by the sequence of digits , and that

Then

Now

and leave the same remainder when divided by

(and of course, as well).

(b) In any three consecutive integers, , one is always a multiple of . And and are primes, and neither nor is a multiple of

And, of course, is even whenever is a prime .

Hence

(c) Consider the remainders when (x-1) and (x+1) are divided by 3, and then use the results of (a).

Grandad