Aurifeuillian Factorization/Examples/2^4n+2 + 1/Historical Note

Historical Note on Aurifeuillian Factorization of $2^{4 n + 2} + 1$

According to David Wells in his Curious and Interesting Numbers, 2nd ed. of $1997$, this identity was established by François Édouard Anatole Lucas, who generalised the result:

$2^{58} + 1 = \paren {2^{29} - 2^{15} + 1} \paren {2^{29} + 2^{15} + 1}$

which had been discovered by Léon-François-Antoine Aurifeuille in $1871$.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2^{58} + 1$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2^{58} + 1$