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 +
Return period interest and formula_5 is the counting rate. If the return period of occurrence is 1 in 234 years (formula_5 = 0.0043) then the probability of no occurrence in ten years is In a given period of "n" years, the probability of a given number "r" of events of a return period formula_5 is given by the binomial distribution as follows. In the limit of :formula_11, such that formula_12 then Take where Given that the return period of an event is 100 years, So the probability that such an event occurs "exactly once" in 10 successive years is: Return period is