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I'm stumbling over this interesting proof:

Show that if $p$ is a prime number, the positive integers less than $p$, except $1$ and $p-1$, can be split into $(p-3)\over2$ pairs of integers such that each pair consists of integers that are inverses of each other modulo $p$.

Any help will be appreciated. Thanks.

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    Shah: Assuming I write to answer, I'm unable to assess what background to assume from the reader. Are you familiar with the basic properties of [congruence notation](http://en.wikipedia.org/wiki/Modular_arithmetic#Congruence_relation) for modular arithmetic?2012-01-03
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    Yes. You may proceed.2012-01-03

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