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N= sum of k positive integers that are relatively prime to N

Source: 2016 Saudi Arabia IMO TST , level 4+, I p1

July 29, 2020
number theorySumcoprime

Problem Statement

Call a positive integer N≥2N \ge 2 special if for every k such that 2≤k≤N,N2 \le k \le N, N can be expressed as a sum of kk positive integers that are relatively prime to NN (although not necessarily relatively prime to each other). Find all special positive integers.
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