Fermat, Euler, Wilson - Three Case Studies in Number Theory
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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.
KeywordsProgram verification Theorem proving by induction Number theory
Thanks to both referees for constructive criticism and suggestions.
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