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RMO KV 2024 Q4

Source: RMO KV 2024 Q4

November 3, 2024

number theory

Problem Statement

Let

n>1

be a positive integer. Call a rearrangement

a_1,a_2, \cdots , a_n

of

1,2, \cdots , n

nice if for every

k = 2 ,3, \cdots , n

, we have that

a_1^2 + a_2^2 + \cdots + a_k^2

is not divisible by

k

. Determine which positive integers

n>1

have a nice arrangement.

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