# [seqfan] Re: Mapping problem

Wed Nov 9 19:51:01 CET 2016

```Thank you, I indeed did not take into account that
there is no n such that n^2==22(mod 25).

Best,

________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Daniel Berend [berend at cs.bgu.ac.il]
Sent: 09 November 2016 16:17
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: Mapping problem

Because 22 is not in the image of the function. If you just wanted the set to be invariant, you could have taken all of \Z(25).

Best,

Dani
________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Vladimir Shevelev [shevelev at exchange.bgu.ac.il]
Sent: Wednesday, November 09, 2016 1:16 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: Mapping problem

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

Best,
________________________________________
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?

--
Seqfan Mailing list - http://list.seqfan.eu/

--
Seqfan Mailing list - http://list.seqfan.eu/

--
Seqfan Mailing list - http://list.seqfan.eu/

```