yeland404 said:Homework Statement
Prove that n ℂ Z+ is divisible by 3( respectively 9). to show that if and only if the sum of its digits is divisible by 3
Homework Equations
The Attempt at a Solution
so n= 3q, q>3 that n[itex]\equiv[/itex]0 mod 3
n=X1* 10^n+ x2*10^n-1...Xn
so need to prove(x1+x2+...Xn)[itex]\equiv[/itex]0 mod 3, the how to prove the next step
Number theory is a branch of mathematics that deals with the properties and relationships of numbers. It involves the study of integers, prime numbers, and their patterns.
A divisible number is a number that can be divided by another number without leaving a remainder. For example, 12 is divisible by 3 because 12 ÷ 3 = 4 with no remainder.
To solve a number theory problem involving divisibility, you need to understand the rules of divisibility. For example, a number is divisible by 2 if it ends in 0, 2, 4, 6, or 8. Once you know the rules, you can use them to determine which numbers are divisible by a given number and solve the problem.
Number theory has numerous real-life applications, such as in cryptography, which involves encoding and decoding messages using prime numbers. It is also used in coding theory, which deals with error-correcting codes in communication systems. Number theory is also used in the fields of physics, computer science, and engineering.
Number theory is important because it helps us understand the fundamental properties of numbers and their relationships. It has practical applications in various fields and has played a crucial role in the development of modern technology. Additionally, number theory helps us solve complex mathematical problems and can lead to new discoveries and innovations.