Number theory · Divisibility · Congruences · Gauss sum · Size estimates
Can the numbers \(1, 2, \dots, 100\) be distributed into three groups so that the sum of the numbers in the first group is divisible by \(102\), the sum of the numbers in the second group is divisible by \(203\), and the sum of the numbers in the third group is divisible by \(304\)?
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Republic Competition (Republicko takmicenje) 2001, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source