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Topic: ------ ------ ------- ------- special prime
Replies: 7   Last Post: May 9, 2013 7:58 PM

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Posts: 821
Registered: 9/1/10
Re: ------ ------ ------- ------- special prime
Posted: May 9, 2013 7:58 PM
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> 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(k-1) =
> y^k(k-1)mod(k^2) (2)
> Since k is prime to xy then both x^k(k-1) and
> y^k(k-1) are congruent
> to 1mod(k^2)
> Therefore, 1^(k-1) = 1mod(k^2) (3)
> Consequently, 2^(k-1) = 1mod(k^2) is impossible.
>
> This implies (1) cannot be satisfied if k is a
> Wieferich Prime.
>
> Any helpful comment will be appreciated.


:helpful+



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