6

Part of 2022 New Zealand MO

Problems(1)

among any k positive integers, one may select even number with sum s, n|s

Source: 2022 NZMO - New Zealand Maths Olympiad Round 1 p6

Let a positive integer

n

be given. Determine, in terms of

n

, the least positive integer

k

such that among any

k

positive integers, it is always possible to select a positive even number of them having sum divisible by

n

number theorydivisibleSum