Difference between revisions 573276532 and 573276624 on enwiki

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)
* x ≡ 4 (mod 11),

the above method would prove to be inefficient. 

The only equality identity that we need is a ≡ b (mod m) is equivalent to a = m'''''k''''' + b, for every '''''k''''' belonging to the '''''set of integers'''''. 

==
='''PROCEDURE'''===
1. Begin by rewriting the first congruence as '''''x = 2a + 1''''', where ''a belongs to the set of integers''.

2. Substitute the expression '''''2a + 1''''' for x in the next congruence to have '''''2a + 1 ≡ 2(mod 3)'''''.

3. Rewrite 2(mod 3) as '''''3a + 2 '''''and solve for a:
(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]]