## hartnn Group Title inverse of mod function? like y= x mod p, 1=5 mod 2 how do i get 5 from {1,2} one year ago one year ago

1. suvesh253 Group Title

doesnot exist as inverse only possible for one-one function

2. mukushla Group Title

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

3. mukushla Group Title

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

4. ganeshie8 Group Title

mod is not 1-1 function

5. suvesh253 Group Title

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

6. hartnn Group Title

c= a mod b = -> corresponds to

7. Mikael Group Title

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...

8. hartnn Group Title

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

9. hartnn Group Title

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

10. Mikael Group Title

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

11. hartnn Group Title

12. hartnn Group Title

like 5 mod 2 is 1

13. suvesh253 Group Title

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

14. estudier Group Title

x = sgn(x) .|x|

15. Mikael Group Title

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

16. Mikael Group Title

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

17. hartnn Group Title

but i didn't understand....

18. Mikael Group Title

thx oh exalted one !

19. Mikael Group Title

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

20. Mikael Group Title

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

21. hartnn Group Title

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

22. Mikael Group Title

Everybody that did - pls gratify

23. satellite73 Group Title

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 $$x$$ ?

24. hartnn Group Title

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

25. Mikael Group Title

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

26. satellite73 Group Title

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

27. Mikael Group Title

No uniqueness - only an IDEAL OF ANSWERS

28. hartnn Group Title

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

29. Mikael Group Title

Yes - they form an IDEAL

30. satellite73 Group Title

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

31. Mikael Group Title

Anyway the set pf answers here IS an Ideal.

32. Mikael Group Title

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

33. hartnn Group Title

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

34. Mikael Group Title

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

35. hartnn Group Title

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

36. Mikael Group Title
37. Mikael Group Title

38. hartnn Group Title

because of those ... i cannot get the reference

39. hartnn Group Title

only last one i couldn't get

40. Mikael Group Title

Just ggle "elementary remainder group theory"