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  • Cited by 2
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Alderson, Helen Popova 1973. On the septimic character of 2 and 3. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 74, Issue. 03, p. 421.

    Karst, Edgar 1967. Tables on fifth power residuacity. BIT, Vol. 7, Issue. 2, p. 114.


On the quintic character of 2

  • Helen Popova Alderson (a1)
  • DOI:
  • Published online: 01 February 2010

Criteria for 2 to be an e-th power residue of a prime

p ≡ 1 (mod e = ef+1,

have been obtained in various forms for e = 2, 3, 5. Euler proved the well known result that 2 is a quadratic residue of a prime p ≡ ± l (mod 8). Dickson [1] showed that 2 is a cubic residue of p ≡ 1 (mod 3) if and only if p = L2+27M2 is soluble in integers L, M.

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1. L. E. Dickson , “Cyclotomy, higher congruences and Waring's problem”, American J. of Math., 57 (1935), 391424.

2. Emma Lehmer , “The quintic character of 2 and 3”, Duke Math. J., 18 (1951), 1118.

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  • ISSN: 0025-5793
  • EISSN: 2041-7942
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