Abstract
Thirty-two unsolved problems in elementary number theory are listed as challenge problems for automated reasoning systems. The clausal forms of the conjectures and of their negations are given, suitable as input to resolution theorem provers versed in Peano arithmetic.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
ApostolT., Introduction to Analytic Number Theory, Springer-Verlag, New York (1976).
DavenportH., The Higher Arithmetic, Dover, New York (1983).
GuyR., Unsolved Problems in Number Theory, Springer Verlag, New York (1981).
HardyG. and WrightW., An Introduction to the Theory of Numbers, 5th edn., Clarendon Press, Oxford (1979).
McCune, W., OTTER 2.0 User's Guide, ANL-90/9, Argonne National Laboratory (1990).
MendelsonE., Introduction to Mathematical Logic, 3rd edn., Wadsworth & Brooks/Cole, Monterey (1987).
Quaife, A., The near certainty of Goldbach's conjecture, unpublished manuscript (1989).
Quaife, A., Automated development of fundamental mathematical theories. PhD Dissertation, University of California at Berkeley (1990).
RibenboimP., The Book of Prime Number Records, Springer-Verlag, New York (1988).
ShanksD., Solved and Unsolved Problems in Number Theory, 3rd edn., Chelsea, New York (1985).
SierpinskiW., Elementary Theory of Numbers, Panstwowe Wydawn. Naukowe, Warsaw (1964).
WagonS., Carmichael's ‘empirical theorem’, Math. Intelligencer 8(2), 61–63 (1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Quaife, A. Unsolved problems in elementary number theory. J Autom Reasoning 7, 287–300 (1991). https://doi.org/10.1007/BF00243812
Issue Date:
DOI: https://doi.org/10.1007/BF00243812