Wieferich pair

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In mathematics, a Wieferich pair is a pair of prime numbers p and q that satisfy

p^{q − 1} ≡ 1 (mod q²) and q^{p − 1} ≡ 1 (mod p²)

Wieferich pairs are named after German mathematician Arthur Wieferich.

The only known Wieferich pairs are (2, 1093), (3, 1006003), (5, 1645333507), (83, 4871), (911, 318917), and (2903, 18787).^[1]

Wieferich pairs play an important role in Preda Mihăilescu's 2002 proof of Mihăilescu's theorem (formerly known as Catalan's conjecture).^[2]

[edit] References

1. ^ Eric W. Weisstein, Double Wieferich Prime Pair at MathWorld.
2. ^ A Cyclotomic Proof of Catalan's Conjecture; Jeanine Daems

[edit] See also

• Wieferich prime