Journal of Automated Reasoning

, Volume 59, Issue 2, pp 267–286 | Cite as

Fermat, Euler, Wilson - Three Case Studies in Number Theory

  • Christoph Walther
  • Nathan Wasser


We report on computer assisted proofs of three theorems from Number Theory, viz. Fermat’s Little Theorem, Euler’s generalization of Fermat’s statement and Wilson’s Theorem. Common to the formal proofs is that permutation of certain number lists has to be proved, which causes the main effort in the development. We give a short survey of the Open image in new window   system used in this experiment and illustrate the proofs before presenting them formally. We also discuss alternative solutions, report on the required effort and conclude with some experiences gained from this experiment.


Program verification Theorem proving by induction Number theory 



Thanks to both referees for constructive criticism and suggestions.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Fachbereich InformatikTechnische Universität DarmstadtDarmstadtGermany

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