In mathematics, a Wieferich pair is a pair of prime numbers p and q that satisfy Wieferich pairs are named after German mathematician Arthur Wieferich.
Wieferich pairs play an important role in Preda Mihăilescu's 2002 proof[1] of Mihăilescu's theorem (formerly known as Catalan's conjecture).
For the smallest Wieferich n-tuple, see OEIS: A271100, for the ordered set of all Wieferich tuples, see OEIS: A317721.
It is a conjecture that every integer k>1 has a periodic Wieferich sequence.
Eventually, it is unknown that values for k exist such that the Wieferich sequence of k is finite.