Talk:Congruence relation

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[edit] Modular arithmetic

The prototypical example is modular arithmetic: for n a positive integer, two integers a and b are called congruent modulo n if a − b is divisible by n."

I think that there is no need to a and b to be a integers. Definition works well if a and b are real numbers with feature "a-b is integer" --Čikić Dragan 13:43, 23 February 2006 (UTC)

Things are most interesting when the numbers are integers, see modular arithmetic. If you are a computer guy, see modulo operation for the real number case. Oleg Alexandrov (talk) 23:20, 23 February 2006 (UTC)

[edit] LinearAlgebra

I'm not familiar enough with the concept of congruence in complex matricies to go ahead and edit this myself, but could "{\scriptstyle *}" congruence be called "{\scriptstyle \dagger}" congrunece for greater clarity. That is, I'm under the impression that {\scriptstyle P^* = P^{\dagger}}.

Kevmitch 01:52, 1 March 2006 (UTC)



i am not good with wiki's math symbols so can someone plz add the following information

a = b(mod n) implies n|(a − b)

and if n X (a - b) then <<a is not congruent to b (mod n)>>

if a = b(mod n) and m|n then it can be proved that (for integer m)

a = b (mod m)

--164.58.59.64 03:11, 26 March 2006 (UTC)faisal

That's in the article titled modular arithmetic, and applies to one, but not all, of the congruence relations considered here. Michael Hardy 03:45, 26 March 2006 (UTC)
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