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Catalan pseudoprime : ウィキペディア英語版
Catalan pseudoprime
In mathematics, a Catalan pseudoprime is an odd composite number ''n'' satisfying the congruence
: (-1)^} \cdot C_} \equiv 2 \pmod n,
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 with the latter two being squares of Wieferich primes. In general, if ''p'' is a Wieferich prime, then ''p''2 is a Catalan pseudoprime.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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