theorem Th24: :: NAT_4:24

for n, f, c being Element of NAT st n - 1 = f * c & f > c & c > 0 & ( for q being Element of NAT st q divides f & q is prime holds
ex a being Element of NAT st
( (a |^ (n -' 1)) mod n = 1 & ((a |^ ((n -' 1) div q)) -' 1) gcd n = 1 ) ) holds
n is prime