Posts:
821
Registered:
9/1/10


Re:     special prime
Posted:
May 9, 2013 7:58 PM


> Consider the following equation under the given > conditions. > > x^k = y^kmod(k^2) (1) > > Conditions: x, y, k are odd integers such that x, y, > k are coprime and > k is a prime > 3. > From (1) one gets (2) where x^k(k1) = > y^k(k1)mod(k^2) (2) > Since k is prime to xy then both x^k(k1) and > y^k(k1) are congruent > to 1mod(k^2) > Therefore, 1^(k1) = 1mod(k^2) (3) > Consequently, 2^(k1) = 1mod(k^2) is impossible. > > This implies (1) cannot be satisfied if k is a > Wieferich Prime. > > Any helpful comment will be appreciated.
:helpful+

