Difficult one

[Guest]

There is a prime number p>3 and some positive integers a,b,c.
We know that a+b+c=p+1 and x=(a^3+b^3+c^3) - 1 is divisible by p.

Proove that at least one of the numbers a,b,c is equal 1...

 

[Guest]

I know that x is odd, because a+b+c is even...

But that's all as far as my solution is concerned