inverse of mod function?
like y= x mod p,
1=5 mod 2
how do i get 5 from {1,2}

- hartnn

inverse of mod function?
like y= x mod p,
1=5 mod 2
how do i get 5 from {1,2}

- schrodinger

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- anonymous

doesnot exist as inverse only possible for one-one function

- anonymous

y=|x| ?
inverse of this will not be a function

- anonymous

inverse exist x=|y| but its not a function

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## More answers

- ganeshie8

mod is not 1-1 function

- anonymous

modulus is a many-one function hence it's inverse not possible

- hartnn

c= a mod b
= -> corresponds to

- anonymous

NO PROBLEMAS SENIOUR @hartnn !
Let B be the set of ordered pairs of pairs-of-numbers, in other words pairs of points in the plane: \[ b \in B \,\,\iff b=(P_1, P_2) \] then the inverse function of \[Abs^{-1}(y) = ((y,y),(y,-y)) \] and a medal , naturally.
forgive my humbleness...

- hartnn

whats and how ?
\(Abs^{-1}(y) = ((y,y),(y,-y))\)

- hartnn

if i have y=x mod 7, how would i find its inverse ?

- anonymous

The Abs is of course |x| not the algebraic coincidence of names.

- hartnn

i eas talking about remainder

- hartnn

like 5 mod 2 is 1

- anonymous

if modulus is with only number then it is one-one and inverse will exist

- anonymous

x = sgn(x) .|x|

- anonymous

Anyway also for remainder possible to invert \[ mod:\,r_{Ideal} \rightarrow r \\ mod^{-1}: r \rightarrow r_{Ideal}\]

- anonymous

and a , the action that should not be asked but anyway received :)

- hartnn

but i didn't understand....

- anonymous

thx oh exalted one !

- anonymous

Learn about Ideals even if you dont have them :)
http://en.wikipedia.org/wiki/Ideal_(ring_theory)

- anonymous

MEdals, Medals gentleman for the wondering scholar ....! Keep them falling !

- hartnn

hmmm...didn't study ideals, i'll go through them, thanks

- anonymous

Everybody that did - pls gratify

- anonymous

i think the question is maybe something different,
are you asking how do you solve
\[x\equiv y (mod n)\] for \(y\) if you know \(x\) ?

- hartnn

yes, i wrote somewhere in between
= -> correcponds to

- anonymous

If that was the question I would not solve it - but it was not!

- anonymous

so for example solve \( 5\equiv x\text{ mod } 3\)

- anonymous

No uniqueness - only an IDEAL OF ANSWERS

- hartnn

there are many (or infinite ?) values of x in 5=x mod 3 ??

- anonymous

Yes - they form an IDEAL

- anonymous

ideals live in arbitrary rings, and are not necessary for understanding elementary number theory

- anonymous

Anyway the set pf answers here IS an Ideal.

- anonymous

By the way the only proper way to make equivalence necessary for "REMAINDER CALCULUS" is bu using ideals. Elementary - well yes.

- hartnn

ok, thank you @Mikael i'll go through IDEALS and ask u if i have any doubts.
thanks to @satellite73 also :)

- anonymous

Firstly is the "cyclical group". It will give you the applications. Only then that. This takes you further

- hartnn

any good reference for such things(other than wikipedia) where these things are explained in lucid manner ?

- anonymous

http://en.wikipedia.org/wiki/Modular_arithmetic

- anonymous

1 mathdl.maa.org/images/upload_library/22/Polya/Brenton.pdf
en.wikipedia.org/wiki/Elementary_group_theory
math.uc.edu/~hodgestj/Abstract%20Algebra/GroupTheory512.pdf
www.rowan.edu/.../Some%20Elementary%20Group%20Theory.pdf

- hartnn

because of those ... i cannot get the reference

- hartnn

only last one i couldn't get

- anonymous

Just ggle "elementary remainder group theory"

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