Английская Википедия:Catalan pseudoprime
Материал из Онлайн справочника
Шаблон:Refimprove In mathematics, a Catalan pseudoprime is an odd composite number n satisfying the congruence
- <math> (-1)^{\frac{n-1}{2}} \cdot C_{\frac{n-1}{2}} \equiv 2 \pmod n,</math>
where Cm denotes the m-th Catalan number. The congruence also holds for every odd prime number n that justifies the name pseudoprimes for composite numbers n satisfying it.
Properties
The only known Catalan pseudoprimes are: 5907, 1194649, and 12327121 Шаблон:OEIS with the latter two being squares of Wieferich primes. In general, if p is a Wieferich prime, then p2 is a Catalan pseudoprime.
References
- Шаблон:Cite journal
- Catalan pseudoprimes. Research in Scientific Computing in Undergraduate Education.
Шаблон:Classes of natural numbers