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3 divides no of lists of jointly coprime positive integer numbers that sum to n

Source: IMAR 2011 p4

September 27, 2018
number theorycoprimeSumdivisible

Problem Statement

Given an integer number n≥3n \ge 3, show that the number of lists of jointly coprime positive integer numbers that sum to nn is divisible by 33. (For instance, if n=4n = 4, there are six such lists: (3,1),(1,3),(2,1,1),(1,2,1),(1,1,2)(3, 1), (1, 3), (2, 1, 1), (1, 2, 1), (1, 1, 2) and (1,1,1,1)(1, 1, 1, 1).)
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