- #1

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## 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

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- Thread starter TheMathNoob
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In summary, congruence mod n means that two numbers have the same remainder when divided by n. In the case of n congruent to 6 mod 5, n is also congruent to 1 mod 5 because 5 divides n-6, and when divided by 5, the remainder is 1. However, in the case of 16 congruent to 2 mod 7, even though 7 divides 16-2, the remainder when dividing by 7 is not 2. Therefore, it is not necessary for b to be a perfect square in order for a^2 to be congruent to b mod n.

- #1

- 189

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if n is congruent to 6 mod 5

then n is congruent to 1 mod 5?

[/B]

This is not a problem. It's a doubt that I have

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- #2

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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

- #3

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x is a number between 0 and 5ehild said:Can you write 6 as congruent to x mod 5? What is x?

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What does it mean that a number n is congruent to x mod 5?

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5 divides n-xehild said:What does it mean that a number n is congruent to x mod 5?

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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

- #7

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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?

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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?

a congruent to b mod n implies that a=kn+b. It follows that a

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