mod 6

[y.kohmoto]

    Don Reble wrote : 
    >If N is an integer, then neither N^2-N+1 nor N^2+N+1 is divisible by
    >any positive number of the form 6k+5.

    I think that the proof is not comprete for A056650.
    The following theorem should be proved.

    T.3^n   p^2+p+1=3^n , p is prime, has no solution.

    Is it true?
    If not, the largest prime factor of x(n-1)^2+x(n-1)+1 may become 3. 
    It doesn't fit the low :
    "Except the first term all terms are 1 mod 6."

    Yasutoshi