MathDB
2017-2018 Spring OMO Problem 17

Source:

April 3, 2018

Problem Statement

Let SS be the set of all subsets of {2,3,…,2016}\left\{2,3,\ldots,2016\right\} with size 10071007, and for a nonempty set TT of numbers, let f(T)f(T) be the product of the elements in TT. Determine the remainder when ∑T∈S(f(T)−f(T)−1)2 \sum_{T\in S}\left(f(T)-f(T)^{-1}\right)^2 is divided by 20172017. Note: For bb relatively prime to 20172017, we say that b−1b^{-1} is the unique positive integer less than 20172017 for which 20172017 divides bb−1−1bb^{-1} -1.
Proposed by Tristan Shin
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