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The Wieferich pair - in the theory of numbers, the pair of prime numbers p and q satisfying the following conditions:

Or alternatively:

The term Wieferich is derived from the name of the German mathematician Arthur Wieferich and is somewhat analogous to the notion of the number of the first Wieferich. So far (2015), only seven such pairs have been found, namely:

Wieferich's pair play a role in the proof of the Mihăilescu theorem, formerly known as the Catalana hypothesis. Bibliography

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