World of my creative work
This category exclusively contains mathematical articles, which either have certain practical application in definite area, or contain some interesting observations.
Properties of modulo operation: : . Lemma “About finiteness of modular-power sequence” Suppose a given certain module , , and a certain integral number , and suppose a defined series of elements , where , , , . Then for the given sequence the condition of repeat is satisfied: , , : . by contradiction:…
Supporting materials: Note: this article uses supporting theorems, such as “Common commutative law” and “About amount of subsets in the given set”. Since I’m yet unable to find their analogues on English-language resources, I’ll cite their statements in this section. Theorem “The common commutative law”: suppose given non-empty set , – associative and commutative binary…
Statement: Suppose a given amount of bits of scrambler . Then there exist scramblers of the length . Proof: Key of the scrambler – certain sequence of bits of the length . After reviewing key as vector of set , it’s possible to make conclusion, that in total there exist keys of the length ….