It’s well known that the geometric mean of a set of positive numbers is less sensitive to outliers than the arithmetic mean. It’s easy to see this by example, but is there a deeper theoretical reas...
Perhaps the best question to start with is " Can modular arithmetic be extended to the rational or real numbers?", which leads us to "What is modular arithmetic?", which I like to think is "The arithmetic of some ring 'passed down' to its quotients, by means of modding by some ideal".
arithmetic - What are the formal names of operands and results for ...
A famous theorem by¹ Fermat is that four squares cannot form an arithmetic progression. (Three definitely can: $1^2 = 1$, $5^2 = 25$ and $7^2 = 49$ already give an example). It already has been dis...
Modular arithmetic utilizes this "wrapping around" idea, after you reached the greatest element comes the smallest. So modular arithmetic is a sort of a mindset. A binary operation is an operation which combines two elements, for example addition is a binary operation since it combines two elements.
- does the proof above make sure that $a_n$ is not arithmetic? a sequence cannot be arithmetic and geometric at the same time, right? 2) what about more complex expressions? like $b_n=ln (n)$? how do I quickly see if it is arithmetic or geometric sequence?
Definitely "The arithmetic of Dynamical Systems" by Silverman is THE textbook you should read first. In my opinion, in order to get a grasp of what arithmetic dynamics is about, you firstly need solid bases of algebraic geometry and number theory. Complex dynamics is also going to be pretty helpful if you want to enter the more dynamical aspects of the theory.