4

Part of India EGMO 2024 TST

Problems(1)

I am always bigger than my index double

Source: India EGMO TST 2024/4

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}

i

(indices are taken

\bmod~ N

). Find all possible

N

for which this is possible.
Proposed by Sutanay Bhattacharya

algebranumber theoryEgmo tst