1

Part of 2019 Serbia National Math Olympiad

Problems(1)

2019 Serbia MO Day 1 P1

Source: 2019 Serbia MO

Find all positive integers

n, n>1

for wich holds : If

a_1, a_2 ,\dots ,a_k

are all numbers less than

n

and relatively prime to

n

a_1<a_2<\dots <a_k

, then none of sums

a_i+a_{i+1}

i=1,2,3,\dots k-1

are divisible by

3

number theoryrelatively prime