View source for 2001 IMO Shortlist Problems/N4

== Problem ==
Let <math>p \geq 5</math> be a prime number. Prove that there exists an integer <math>a</math> with <math>1 \leq a \leq p - 2</math> such that neither <math>a^{p - 1} - 1</math> nor <math>(a + 1)^{p - 1} - 1</math> is divisible by <math>p^2</math>.

== Solution ==
{{solution}}

== Resources ==

* [[2001 IMO Shortlist Problems]]
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17473 Discussion on AOPS/MathLinks]

[[Category:Olympiad Number Theory Problems]]