Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. The basic objective of Arithmetical dynamics is to explain the arithmetic properties with regard to underlying geometry structures. Again, we are here with the Part 5 of the Arithmetical Dynamics Series. Let's get started.... And suppose that R has no periodic points […]
Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. We are here with the Part 0 of the Arithmetical Dynamics Series. Let's get started.... Rational function \( R(z)= \frac {P(z)}{Q(z)} \) ; where P and Q are polynimials . There are some theory about fixed points . Theorem: Let \( \rho […]
This is an interesting and cute sum based on the concept of Arithematic and Geometric series .The problem is to find a solution of a probability sum.
This is a cute and interesting problem based on System of the linear equation in linear algebra. Here we are finding the determinant value .
Arithmetic Mean and Geometric Mean inequality form a foundational principle. This problem from I.S.I. Entrance is an application of that.
হাইপারবোলিক জ্যামিতির জগৎটা একদমই অন্যরকম। এখানে ইউক্লিড খুঁড়িয়ে খুঁড়িয়ে হাঁটেন। এখানে সমান্তরাল রেখা মিশে যায়। এখানে সরলরেখা দেখায় আঁকা বাঁকা।
Suppose you are given a Number Theory Olympiad Problem. You have no idea how to proceed. Totally stuck! What to do? This post will help you to atleast start with number theory problem. You will have something to proceed. But as we share in our classes, how to proceed towards any problem generally comprises of […]
The inverse of a number (modulo some specific integer) is inherently related to GCD (Greatest Common Divisor). Euclidean Algorithm and Bezout's Theorem forms the bridge between these ideas. We explore these beautiful ideas.
We are here with the Part 4 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. $P^{m}(z)=z$ and $P^{N}(z)=z$ where $m\left|N \Rightarrow\left(P^{m}(z)-z\right)\right|\left(P^{N}(z)-z\right)$ The proof of the theorem in Part 0 : Let , P be the polynomials satisfying the hypothesis of theorem 6.2.1 […]
We are here with the Part 3 of the Arithmetical Dynamics Series. Let's get started.... Arithmetical dynamics is the combination of dynamical systems and number theory in mathematics. Theory: Let \( \{ \zeta_1 , ......., \zeta_m \} \) be a ratinally indifferent cycle for R and let the multiplier of \( R^m \) at each […]