[seqfan] Re: Mapping problem

Vladimir Shevelev shevelev at bgu.ac.il
Wed Nov 9 12:16:54 CET 2016

Maybe I missed something, but why we cannot consider
as the largest subset S(25)={0,1,6,9,11,16,21,22}?

From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of David Wilson [davidwwilson at comcast.net]
Sent: 09 November 2016 05:46
To: 'Sequence Fanatics Discussion list'; 'math-fun'
Subject: [seqfan] Mapping problem

Let S(n) be the largest subset of Z(n) fixed by the mapping n -> n^2, and
let f(n) = |Z(n)|.
For example, S(25) = {0, 1, 6, 11, 16, 21} is the largest set of residues
modulo 25 fixed by the mapping n -> n^2, so f(25) = |S(25)| = 6.
Can you find a formula for f(n) in terms of n?

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