- #1
TheMathNoob
- 189
- 4
Homework Statement
if n is congruent to 6 mod 5
then n is congruent to 1 mod 5?
Homework Equations
The Attempt at a Solution
[/B]
This is not a problem. It's a doubt that I have
Can you write 6 as congruent to x mod 5? What is x?TheMathNoob said:Homework Statement
if n is congruent to 6 mod 5
then n is congruent to 1 mod 5?
Homework Equations
The Attempt at a Solution
[/B]
This is not a problem. It's a doubt that I have
x is a number between 0 and 5ehild said:Can you write 6 as congruent to x mod 5? What is x?
5 divides n-xehild said:What does it mean that a number n is congruent to x mod 5?
Yes, but you said that x must be between 0 and 5. Which number is x if n=6?TheMathNoob said:5 divides n-x
TheMathNoob said:5 divides n-x
I got it by algebra 5 divides n-6 so n-6=5k, n=5(k+1)+1, so 5 divides n-1 which implies n is congruent to 1 mod 5. I am having another inquiry with my friend. He claims that 16 is not congruent to 2 mod 7 because he thinks that a^2 congruent to b mod n implies that b has to be a perfect square. Is that correct?ehild said:Yes, but you said that x must be between 0 and 5. Which number is x if n=6?
Correct.TheMathNoob said:I got it by algebra 5 divides n-6 so n-6=5k, n=5(k+1)+1, so 5 divides n-1 which implies n is congruent to 1 mod 5.
TheMathNoob said:I am having another inquiry with my friend. He claims that 16 is not congruent to 2 mod 7 because he thinks that a^2 congruent to b mod n implies that b has to be a perfect square. Is that correct?
Modular arithmetic is a branch of mathematics that deals with the remainder after dividing two numbers. It is often used in cryptography and computer science to solve problems involving repeating patterns or cycles.
Congruence modulo 5 is a specific type of modular arithmetic where the numbers are divided by 5 and the remainder is considered. Two numbers are said to be congruent modulo 5 if they have the same remainder when divided by 5.
Modular arithmetic is used in various fields such as computer science, cryptography, and number theory. It is often used to solve problems involving repeating patterns or cycles, in encryption algorithms, and in identifying patterns in data.
Congruence modulo 5 has various applications in real-world problems. It is used in clock arithmetic, where the numbers on a clock repeat every 12 hours or 24 hours. It is also used in music theory to identify repeating patterns and in coding theory to detect errors in transmitted data.
In regular arithmetic, the quotient and remainder are both considered when dividing two numbers. In congruence modulo 5, only the remainder is considered. This means that numbers that are normally considered different in regular arithmetic can be considered congruent modulo 5. For example, 22 and 17 are not equal in regular arithmetic, but they are congruent modulo 5 because they both have a remainder of 2 when divided by 5.