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Old 2014-07-14, 23:30   #2
Zeta-Flux
 
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May 2003

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Better than that, the Wieferich condition is equivalent to 2^{(p-1)/2} \equiv \pm 1\pmod{p^2}. This makes it slightly easier to test for the condition.

The only place I know of where the Wieferich condition is really useful is in the first case of Fermat's last theorem and in the solution to Catalan's conjecture.
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