Practice Questions on Euler’s Theorem
Q1: Find the remainder when 250 is divided by 11.
Q2: Calculate the remainder when 5100 is divided by 17.
Q3: Determine the remainder when 375 is divided by 13.
Q4: Find the remainder when 440 is divided by 9.
Q5: Find the remainder when 1025 is divided by 8.
Euler’s Theorem
Euler’s Theorem states that for any integer a that is coprime with a positive integer m, the remainder of aϕ(m) divided by m is 1. We focus on proving Euler’s Theorem because Fermat’s Theorem is essentially a specific instance of it. This relationship arises because when p is a prime number, ϕ(p) equals p-1, thus making Fermat’s Theorem a subset of Euler’s Theorem under these conditions.
Euler’s theorem is a fundamental result in number theory, named after the Swiss mathematician Leonhard Euler. It states a relationship between the number theory functions and concepts of modular arithmetic. In this article, we will discuss Euler’s Theorem, including its statement and proof.
Table of Content
- What is Euler’s Theorem?
- Euler’s Theorem Formula
- Historical Background of Euler’s Theorem
- Proof of Euler’s Theorem
- Applications of Euler’s Theorem
- Euler’s Theorem Examples
- Practice Questions on Euler’s Theorem