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 +
United States National Physics Olympiad United States National Physics Olympiad The United States National Physics Olympiad (USAPhO) is a high school physics competition run by the American Association of Physics Teachers and American Institute of Physics to select the team to represent United States at the International Physics Olympiad (IPhO). The team is selected through a series of exams testing their problem solving abilities. Approximately the top 20 finalists are invited to a rigorous study camp at University of Maryland to prepare for the IPhO. The International Physics Olympiad began in 1967 among Eastern European countries and many western countries soon joined in the 1970s.