Question

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

Answer 1

doesnot exist as inverse only possible for one-one function

Answer 2

y=|x| ?

inverse of this will not be a function

Answer 3

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

Answer 4

mod is not 1-1 function

Answer 5

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

Answer 6

c= a mod b
= -> corresponds to

Answer 7

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...

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

i eas talking about remainder

Answer 12

like 5 mod 2 is 1

Answer 13

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

Answer 14

x = sgn(x) .|x|

Answer 15

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

Answer 16

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

Answer 17

but i didn't understand....

Answer 18

thx oh exalted one !

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

Everybody that did - pls gratify

Answer 23

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 \(x\) ?

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

No uniqueness - only an IDEAL OF ANSWERS

Answer 28

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

Answer 29

Yes - they form an IDEAL

Answer 30

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

Answer 31

Anyway the set pf answers here IS an Ideal.

Answer 32

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

Answer 33

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

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

because of those ... i cannot get the reference

Answer 39

only last one i couldn't get

Answer 40

Just ggle "elementary remainder group theory"