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Aurifeuillian factorizations

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Aurifeuillean factorizations[1] are derived from the quadratic equation

They are named after Léon-François-Antoine Aurifeuille, who in 1873 rediscovered that

(see A207262). Perhaps Aurifeuille was unaware of Leonhard Euler's August 28, 1742 letter to Christian Goldbach mentioning the identity , which is a broader class of these numbers.

Another Aurifeuillean factorization is

Notes

  1. "Aurifeuillean factorization" is the usual spelling, although Wikipedia uses Aurifeuillian factorization.

References

  • P. H. Fuss, Correspondance math. et physique 1 (1843) p. 145
  • Don Knuth, Seminumerical Algorithms, 3rd ed p392
  • David Wells, Prime Numbers: The Most Mysterious Figures in Math. Hoboken, New Jersey: John Wiley & Sons (2005) p. 15.