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Sum of coprime residues modulo n

Source: Abelkonkurransen Finale 2024, Problem 1a

March 8, 2024
number theorynumber theory proposedmodular arithmeticcoprimecoprime numbers

Problem Statement

Determine all integers n≥2n \ge 2 such that n∣sn−tnn \mid s_n-t_n where sns_n is the sum of all the integers in the interval [1,n][1,n] that are mutually prime to nn, and tnt_n is the sum of the remaining integers in the same interval.
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