Tag: factors

Euler's Theorem, the Totient Function, and Calculating Totients By Hand

Posted in Mathematics


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Today we're going to delve into a little bit of number theory.

In number theory, we are usually dealing with modular arithmetic - expressions of the form:

$$ a \equiv b \mod m $$


$$ f(x) \equiv 0 \mod m $$

The mod indicates we're doing modular arithmetic, which is (formally) an algebraic system called a ring, which consists of the integers 0 through m.

An analogy to modular arithmetic is the way that the sine and cosine function "wrap around," and

$$ \sin \left …

Tags:    mathematics    factors    number theory    euler   

Project Euler Problem 1

Posted in Mathematics


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Overview: The Problem

Project Euler is a website that provides mathematically-oriented programming problems. There are many (over 500) and they are a rich source of profound mathematical insights.

I have been considering a writeup that goes deep into a particular problem, so why not do it with problem 1?

Problem 1 of Project Euler asks:

Find the sum of all the multiples of 3 or 5 below 1000.

It is a pretty simple task - one of the first things covered in a decent programming course is the …

Tags:    computer science    mathematics    factors    sequences    euler    project euler