MathDB

I am always bigger than my index double

Source: India EGMO TST 2024/4

December 31, 2023

algebranumber theoryEgmo tst

Problem Statement

Let

N \geq 3

be an integer, and let

a_0, \dots, a_{N-1}

be pairwise distinct reals so that

a_i \geq a_{2i}

for all

i

(indices are taken

\bmod~ N

). Find all possible

N

for which this is possible.
Proposed by Sutanay Bhattacharya