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A sum and a product give the same remainder

Source: Russian TST 2015, Day 10 P2 (Group NG)

April 21, 2023
number theoryprime numbers

Problem Statement

Let p⩾5p\geqslant 5 be a prime number. Prove that the set {1,2,…,p−1}\{1,2,\ldots,p - 1\} can be divided into two nonempty subsets so that the sum of all the numbers in one subset and the product of all the numbers in the other subset give the same remainder modulo pp{}.
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