When 100/(p-1)=t in Z

then:

1^100 + 2^100 + ... +(p-1)^100 = -1(mod p)

So, the primes are:

2,3,5,11, and... 101

================================

Let be prime number:

if

or:

if

Proof:

Suppose so to every witch is co-prime to :

Hence,

Now, suppose , and primitive root of .

hence, congruent modulo to in some order.

Prove by yourself now that: is also system of congruent modulo .

Hence: