### Abstract

In 1927, Lehmer presented criterions for primality, based on the converse of Fermat's litte theorem. This work formalizes the second criterion from Lehmer's paper, a necessary and sufficient condition for primality.

As a side product we formalize some properties of Euler's phi-function, the notion of the order of an element of a group, and the cyclicity of the multiplicative group of a finite field.

### License

BSD License

### Topics

- Mathematics/Number theory

### Session Lehmer

- Lehmer

### Used by

- Pratt’s Primality Certificates

## Cite

×

Lehmer-AFP

    @article{Lehmer-AFP,
      author  = {Simon Wimmer and Lars Noschinski},
      title   = {Lehmer's Theorem},
      journal = {Archive of Formal Proofs},
      month   = {July},
      year    = {2013},
      note    = {\url{https://isa-afp.org/entries/Lehmer.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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