Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

On numbers of the form $ n^{4}+1$


Author: Daniel Shanks
Journal: Math. Comp. 15 (1961), 186-189
MSC: Primary 10.00
DOI: https://doi.org/10.1090/S0025-5718-1961-0120184-6
Corrigendum: Math. Comp. 16 (1962), 513-513.
MathSciNet review: 0120184
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] Daniel Shanks, ``On the conjecture of Hardy and Littlewood concerning the number of primes of the form $ {n^2} + a$,'' Math. Comp., v. 14, 1960, p. 321-332. MR 0120203 (22:10960)
  • [2] Daniel Shanks, ``A note on Gaussian twin primes,'' Math. Comp., v. 14, 1960, p. 201-203. MR 0111724 (22:2586)
  • [3] A. Gloden, ``A note on factors of $ {n^4} + 1$,'' Math. Comp., v. 14, 1960, p. 278-279. Also see RMT 42, Math. Comp., v. 14, 1960, p. 284. For earlier bibliography see RMT 109, MTAC, v. 11, 1957, p. 274, and RMT 2, MTAC, v. 12, 1958, p. 63. MR 0121332 (22:12071)
  • [4] L. E. Dickson, History of the Theory of Numbers, Stechert, New York, 1934, v. 1, p. 381. According to Dickson, Euler (1752) gave $ {P_1}(1500) = 161$, which is correct, and $ {Q_1}(34) = 8$, which is incorrect--he omits the prime $ {28^4} + 1$.
  • [5] Daniel Shanks, ``A sieve method of factoring numbers of the form $ {n^2} + 1$,'' MTAC, v. 13, 1959, p. 78-86. MR 0105784 (21:4520)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 10.00

Retrieve articles in all journals with MSC: 10.00


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1961-0120184-6
Article copyright: © Copyright 1961 American Mathematical Society

American Mathematical Society