Editing Fermat's little theorem (section)

== Converse{{Anchor|Lehmer's theorem}} ==
The [[Logical converse|converse]] of Fermat's little theorem fails for [[Carmichael number]]s. However, a slightly weaker variant of the converse is '''Lehmer's theorem''':

If there exists an integer {{mvar|a}} such that
<math display="block"> a^{p-1}\equiv 1\pmod p </math>
and for all primes {{mvar|q}} dividing {{math|''p'' &minus; 1}} one has
<math display="block"> a^{(p-1)/q}\not\equiv 1\pmod p, </math>
then {{mvar|p}} is prime.

This theorem forms the basis for the [[Lucas primality test]], an important [[primality test]], and Pratt's [[primality certificate]].