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Sum of products of three integers

Source: Indonesian Mathematical Olympiad 2013 Problem 4

September 5, 2013
modular arithmeticnumber theory unsolvednumber theory

Problem Statement

Suppose p>3p > 3 is a prime number and S=∑2≤i<j<k≤p−1ijkS = \sum_{2 \le i < j < k \le p-1} ijk Prove that S+1S+1 is divisible by pp.
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