Difference between revisions 573276761 and 573276830 on enwiki

< previous diff
next diff >
Method of successive substitution
In [[modular arithmetic]], the '''method of successive substitution''' is a method of solving problems of [[simultaneous congruences]] by using the definition of the congruence equation. It is commonly applied in cases where the conditions of the [[Chinese remainder theorem]] are not satisfied.

There is also an unrelated numerical-analysis method of successive substitution, a [[randomized algorithm]] used for [[root finding]], an application of [[fixed-point iteration]].

(contracted; show full)Expand:
: ''x'' = 11 + 12''k''
to obtain the solution

''x'' ≡ 11 (mod 12)

==='''Example Two (''An Easier Method)'''''===
Although the above method is correct, some of the steps are arbitrary and superfluous. If we had a problem that had these four
  congruences
* x ≡ 1 (mod 2)

* x ≡ 2 (mod 3)

* x ≡ 3 (mod 5)

* x ≡ 4 (mod 11),
(contracted; show full)* [[simultaneous equations]]

[[Category:Modular arithmetic]]

http://en.wikibooks.org/wiki/Discrete_Mathematics/Modular_arithmetic
[[Category:Back Substitution]]
[[Category:Modular Arithmetic]]
[[Category:Modular Congruences]]