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Zeta-Flux · 2014-07-14, 23:30

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.

2014-07-14, 23:30	#2
Zeta-Flux May 2003 7·13·17 Posts	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.