Editing Fermat number (section)

==Pseudoprimes and Fermat numbers==
Like [[composite number]]s of the form 2<sup>''p''</sup> − 1, every composite Fermat number is a [[strong pseudoprime]] to base 2. This is because all strong pseudoprimes to base 2 are also [[Fermat pseudoprime]]s – i.e.,

:<math>2^{F_n-1} \equiv 1 \pmod{F_n}</math>

for all Fermat numbers.<ref>{{Cite book |last=Schroeder |first=M. R. |url=https://www.worldcat.org/title/ocm61430240 |title=Number theory in science and communication: with applications in cryptography, physics, digital information, computing, and self-similarity |date=2006 |publisher=Springer |isbn=978-3-540-26596-2 |edition=4th |series=Springer series in information sciences |location=Berlin ; New York |pages=216 |oclc=ocm61430240}}</ref>

In 1904, Cipolla showed that the product of at least two distinct prime or composite Fermat numbers <math>F_{a} F_{b} \dots F_{s},</math> <math>a > b > \dots > s > 1</math> will be a Fermat pseudoprime to base 2 if and only if <math>2^s > a </math>.<ref>{{cite book|url=https://books.google.com/books?id=hgfSBwAAQBAJ&q=cipolla+fermat+1904&pg=PA132|title=17 Lectures on Fermat Numbers: From Number Theory to Geometry|first1=Michal|last1=Krizek|first2=Florian|last2=Luca|first3=Lawrence|last3=Somer|date=14 March 2013|publisher=Springer Science & Business Media|access-date=7 April 2018|via=Google Books|isbn=9780387218502}}</ref>