PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (194)
Orphanage
Unclass'd
Unproven (498)
Corrections (25)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: High Entry average rating: Medium
automorphic number (Definition)

Given a base $ b$ integer

$\displaystyle n = \sum_{i = 1}^k d_ib^{i - 1}$
where $ d_1$ is the least significant digit and $ d_k$ is the most significant, if it's also the case that the $ k$ least significant digits of $ mn^2$ are the same of those of $ n$, then $ n$ is called an automorphic number, or an $ m$-automorphic number.

Neither $ b$ nor $ b + 1$ can be 1-automorphic in base $ b$.



"automorphic number" is owned by CompositeFan. [ owner history (1) ]
(view preamble)

View style:


Attachments:
examples of 1-automorphic numbers (Example) by PrimeFan
trimorphic number (Definition) by CompositeFan
Log in to rate this entry.
(view current ratings)

Cross-references: least significant digit, integer, base
There are 2 references to this entry.

This is version 2 of automorphic number, born on 2006-10-23, modified 2006-10-24.
Object id is 8469, canonical name is AutomorphicNumber.
Accessed 690 times total.

Classification:
AMS MSC: 11A63 (Number theory :: Elementary number theory :: Radix representation; digital problems)
Pending Errata and Addenda
None.
[ View all 1 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)