Difference between revisions 629234092 and 644668518 on enwiki

{{Original research|date=September 2014}}
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.

(contracted; show full)
* '''x = 30c + 23 '''
* '''= 30(11d + 10) + 23'''
* '''= 330d + 323.'''
'''∴ 330d + 323 '''represents all solutions that satisfies the system of congruences with which we began.

====Checking Our Work====

To check that our answer is correct, we deduce whether each respective residue is conceived when we compute 
2323 by the modulo of each congruence:

323 ≡ '''1''' (mod 2)
* 323 = 161 * 2''' '''+ '''1'''
323 ≡ '''2''' (mod 3)
* 323 = 107 * 3 + '''2'''
323 ≡ '''3''' (mod 5)
* 323 = 64 * 5 + '''3'''
(contracted; show full)
==External links==
* [http://maciejkus.com/chinese_remainder/ A method of successive substitution calculator]

[[Category:Modular arithmetic]]
[[Category:Back Substitution]]
[[Category:Modular Arithmetic]]
[[Category:Modular Congruences]]