Wieferich pair
From Wikipedia, the free encyclopedia
In mathematics, a Wieferich pair is a pair of prime numbers p and q that satisfy
- pq − 1 ≡ 1 (mod q2) and qp − 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
- ^ Eric W. Weisstein, Double Wieferich Prime Pair at MathWorld.
- ^ A Cyclotomic Proof of Catalan's Conjecture; Jeanine Daems
