Method of successive substitution 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. The method of successive substitution is also known as back substitution. Consider the simple set of simultaneous congruences Now, for "x" ≡ 3 (mod 4) to be true, "x" = 3 +
International Linguistics Olympiad International Linguistics Olympiad The International Linguistics Olympiad (IOL) is the fourth newest of a group of twelve International Science Olympiads. Its abbreviation IOL is deliberately chosen not to correspond to the name of the organization in any particular language, and member organizations are free to choose for themselves how to designate the competition in their own language. This olympiad furthers the fields of mathematical, theoretical, and descriptive linguistics. The setup differs from most of the other Science Olympiads, in that the olympiad contains both individual and team contests. The individual contest consists of 5 problems, covering the main fields of